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Topic: BCH code

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In the News (Mon 19 Nov 18)

  BCH code
A multilevel, cyclic, error-correcting, variable-length digital code used to correct errors up to approximately 25% of the total number of digits.
Note: BCH codes are not limited to binary codes, but may be used with multilevel phase-shift keying whenever the number of levels is a prime number or a power of a prime number, such as 2, 3, 4, 5, 7, 8, 11, and 13.
A BCH code in 11 levels has been used to represent the 10 decimal digits plus a sign digit.
www.ebroadcast.com.au /lookup/encyclopedia/bc/BCH_code.html   (84 words)

 Code - Wikipedia, the free encyclopedia
In communications, a code is a rule for converting a piece of information (for example, a letter, word, or phrase) into another form or representation, not necessarily of the same type.
Code words were chosen for various reasons: length, pronounceability, etc. Meanings were chosen to fit perceived needs: commercial negotiations, military terms for military codes, diplomatic terms for diplomatic codes, any and all of the preceding for espionage codes,...
In mathematics, a Gödel code was the basis for the proof of Gödel's incompleteness theorem.
en.wikipedia.org /wiki/Code   (691 words)

 - June 1999 - Building Blocks
BCH are a large and important class of codes in and of themselves.
Some BCH codes are also of known weight distribution (the number of vectors of a given weight [number of 1s for binary], are important for error detection analysis).
BCH codes are rooted in linear algebraic equations and the properties of those equations.
www.commsdesign.com /main/1999/06/9906building.htm   (2673 words)

 13. Properties and Generalizations of our BCH Codes
BCH codes can be used to handle such errors in two ways.
BCH codes with coefficients that are themselves polynomials are called Reed-Solomon codes, and.they are often used to handle burst errors.
On the other hand, the number of code words within a distance E of the message is proportional to a binomial coefficient.
www-math.mit.edu /18.310/properties_bch_codes.html   (3377 words)

 BCH Codes for Error Correction in Transmission of Binary Data An Application of Mathematical Groups to Structures of ...
BCH codes are a family of error-correcting codes discovered by Bose and Ray-Chaudhuri [1960a; 1960b] and independently by Hocquenghem [1959].
To apply a BCH code, a binary message sequence is treated as a list of coef- Þcients of a polynomial; the coefÞcients are binary digits 0 and 1 under modulo 2 arithmetic.
A BCH code is linear and cyclic and prescribes a way of constructing the generator polynomial.
www.comap.com /product/?idx=655   (278 words)

 Microprocessor based BCH decoder - Patent 4856004
Transmitted data are often encoded using error correcting codes to maximize a probability of a data receiver obtaining precisely the data that a data transmitter intends to transmit.
A BCH encoding process adds the remaining 10 bits to permit a BCH decoder to correct three or fewer errors which may occur in the 15-bit block of data.
Since it is a microprocessor based BCH decoder, it is relatively inexpensive, flexible, reliable, and utilizes a relatively small amount of power due to the low number of parts required for construction for such a microprocessor based system.
www.freepatentsonline.com /4856004.html   (6441 words)

 ACM Ubiquity - Software Implemented Fault Tolerance through Data Error Recovery
BCH codes are another cyclic coding scheme for error detection and correction.
RS codes are block-based error correction codes commonly used for massive storage media such as CD, DVD, etc. The proposed scheme aims to supplement the conventional ECC codes.
A bounded distance algorithm is usually employed in decoding block codes and, it is generally hard to use soft decision decoding for block codes.
www.acm.org /ubiquity/views/v6i35_kumar.html   (2669 words)

 Basic procedures for Cyclic, Hamming, Binary Reed-Muller, BCH, Golay codes   (Site not responding. Last check: 2007-11-02)
We give a program which returns all the codewords in a code and all the codewords in its dual code, provided the prime p and the generator matrix are given.
The dual code of this Hamming (7,4) code is a simplex (7,3) code.
This new polynomial is the generating polynomial of the BCH code.
web.usna.navy.mil /~wdj/codes.html   (933 words)

 Highland Communications Technologies
BCH code is a binary linear systematic block code based on finite field theory.
BCH codes defined on both GF(2^14) and GF(2^16) fields with different code lengths and data lengths are used as the outer code for channel coding.
The BCH code developed by Highland Communications Technologies is fully compliant with the DVB_S2 standard.
www.highlandcomm.com /bch_codes/bch_dvb_s2.htm   (313 words)

 BCH code - Wikipedia, the free encyclopedia
A BCH (Bose, Ray-Chaudhuri, Hocquenghem) code is a much studied code within the study of coding theory and more specifically error-correcting codes.
In technical terms a BCH code is a multilevel, cyclic, error-correcting, variable-length digital code used to correct multiple random error patterns.
BCH codes may also be used with multilevel phase-shift keying whenever the number of levels is a prime number or a power of a prime number.
en.wikipedia.org /wiki/BCH_code   (699 words)

 [No title]
A (binary) code $C$ is a subset of $V\coloneq{F}\sb 2\sp n$; the covering radius $R(C)$ of $C$ is the least integer $r$ such that the spheres of radius $r$ in the Hamming metric centered at the points of $C$ cover $V$.
After a short chapter, mostly on BCH codes, they devote a chapter to perfect codes, proving that any nontrivial perfect code over $F\sb q$ has the parameters of one of the well-known perfect codes.
A code is called a weighted covering if the density at each point is at least one." If the density is exactly 1 at each point, the code is called a perfect weighted covering code.
www.eng.tau.ac.il /~litsyn/skip.html   (1787 words)

 BCH Codes
In fact, it can be proven thata single error-correcting BCH code is isomorphic to a Hamming Code, which is a single error correcting linear code.
Because we have defined a BCH code to be cyclic we get the complete generating matrix from cyclic shifts of the generating code vector.
One of the advantages of this type of code is that there is a relatively simple way to decode.
www-math.cudenver.edu /~rrosterm/crypt_proj/node8.html   (411 words)

 Families of Linear Codes
This function constructs the BCH code of designated distance d as the cyclic code with generator polynomial g(x) = lcm{ m_1(x),..., m_(d - 1)(x)} where m_i(x) is the minimum polynomial of alpha^(b + i - 1).
The BCH code is an [n, >= (n - m(d - 1)), >= d] code over K. If b is omitted its value is taken to be 1, in which case the corresponding code is a narrow sense BCH code.
The construction is similar to that of a doubly circulant code except that the first p rows are extended by a mod 2 while the p + 1-th row is extended by b mod 2.
www.math.niu.edu /help/math/magmahelp/text1194.html   (1320 words)

 THE DESIGN OF A VHDL BASED SYNTHESIS TOOL FOR BCH (Bose, Chaudhuri and Hocquenghem) CODECS - Thesis
BCH codes operate over algebraic structures called finite fields and there exist a multitude of decoding algorithms for these codes.
This data concerns the parameters of the code, the structures of the finite field arithmetic operators and the most appropriate decoding algorithm for the code being considered.
By these means the developed BCH codecs are as hardware efficient as hand-crafted ones but are generated in a fraction of the time.
galaxy.uci.agh.edu.pl /~jamro/bch_thesis/bch_thesis.html   (761 words)

 BCH Decoder (Communications Blockset)   (Site not responding. Last check: 2007-11-02)
The BCH Decoder block recovers a binary message vector from a binary BCH codeword vector.
If the BCH code has message length K and codeword length N, then the input has length N and the first output has length K. If the input is frame-based, then it must be a column vector.
The second output is the number of errors detected during decoding of the codeword.
www-rohan.sdsu.edu /doc/matlab/toolbox/commblks/ref/bchdecoder.html   (295 words)

 The Merchant Shipping (BCH Code) (Amendment) Regulations 1994
They bring into effect amendments to the BCH Code which were adopted by the Marine Environment Protection Committee of the International Maritime Organization ("IMO") on 30th October 1992 by Resolution MEPC.56(33).
The adopted amendments mean that the substances to which the requirements of the BCH Code apply are now identified solely by reference to the IBC Code, Chapter 17.
The agreement relevant to these Regulations which modifies an agreement of the description mentioned is Resolution MEPC 56(33) adopting amendments to the BCH Code mentioned in Annex II to the International Convention for the Prevention of Pollution from Ships 1973 and its Protocol of 1978).
www.opsi.gov.uk /si/si1994/Uksi_19942084_en_1.htm   (1068 words)

Observe that since the weight of the generator is 7, the minimum distance of this code is exactly 7; the code can correct up to three errors.
If you understand the structure of what you did for the CRC code, you are most of the way there already.
Since the code is linear, go ahead and assume that the all-zero code word is sent, and simply generate the error pattern.
www.engineering.usu.edu /classes/ece/7670/prog5/prog5.html   (570 words)

 GAP Manual: 65.78 BCHCode   (Site not responding. Last check: 2007-11-02)
of the code and the size q of the field must be relatively prime.
Special cases are =1 (resulting codes are called narrow-sense BCH codes), and =q^m-1 (known as primitive BCH codes).
The true minimum distance of the code is greater than or equal to the Bose distance.
www-groups.dcs.st-and.ac.uk /gap/Gap3/Manual3/C065S078.htm   (190 words)

 decode (Communications Toolbox)
when the coding method is not convolutional code and the code is a binary vector.
Errors are added to the first two bits of the first codeword and the first bit of the second codeword.
k = 5; % Valid message length for BCH code when n = 15 t = 3; % Corresponding error-correction capability msg = ones(10,1); % Two messages, five bits each code = encode(msg,n,k,'bch'); % Encode the message.
radio.feld.cvut.cz /Docs4Soft/matlab/toolbox/comm/decode.html   (587 words)

 Error-correcting codes in MAPLE   (Site not responding. Last check: 2007-11-02)
There are several other procedures of minor importance which we leave to the partially documented code, codes.mpl.
There are 7 code words of weight 3, 7 code words of weight 4, and no code words of weights 1,2, 5 or 6.
A BCH code is a cyclic code which included the binary Hamming codes as a special case.
web.usna.navy.mil /~wdj/codes.htm   (814 words)

 Linear and Cyclic Codes
There are many different varieties of linear codes, such as the well known Hamming codes.
Then we will define BCH codes, which are a specific type of cyclic code.
corresponds to a cyclic shift of the corresponding code vector and multiplication by a polynomial is thus a linear combination of the codevectors in the generating matrix and all of their cyclic shifts.
www-math.cudenver.edu /~rrosterm/crypt_proj/node3.html   (547 words)

 BCH Codec for Long Block Lengths | CRC
Since the processing varies depending on the number of errors in the codeword, we present the decoding speed that was achieved when the codeword has a specified number of errors.
As speed is sometimes more important than flexibility, we optimized the code to handle the case of BCH(n,n-192) where the maximum block length, n, is 65535.
The decoder was benchmarked under the same conditions as the general decoder and the speed results are shown in Table 2.
www.crc.ca /en/html/fec/home/bch/bch?pfon=yes   (416 words)

 Definition of a Code
We define the ternary Golay code as a six-dimensional subspace of the vector space K^((11)), where K is GF(3).
We construct the length 23 Golay code over GF(2) as a cyclic code by factorizing the polynomial x^(23) - 1 over GF(2) and constructing the cyclic code generated by one of the factors of degree 11.
Given a positive integer d, and an integer b >= 1, this function constructs the BCH code of designated distance d having generator polynomial g(x) = lcm{ m_1(x),..., m_(d - 1)} where m_i(x) is the minimum polynomial of alpha^(b + i - 1), for i = 1,..., d - 1.
www.math.wisc.edu /help/magma/text675.html   (1917 words)

 BCH.html   (Site not responding. Last check: 2007-11-02)
This procedure produces a generator polynomial for a BCH code by having
is the integer used to define the code.
Note that the code in question consists of multiples of the polynomial g defined below.
www.math.nmsu.edu /~pmorandi/math431s02/BCH.html   (426 words)

 The Error Correcting Codes (ECC) Page
This BCH code is used in control channels for cellular TDMA in the U.S. Since this code has only two-error correcting capability, fast decoding is done by pre-solving a system of two equations (the syndromes) in two unknowns (the error positions), see MacWilliams and Slone's book, chapter 3.
This BCH code is used in the POCSAG protocol specification for pagers.
This is a C++ program (compiled for Sparcs) that computes properties of binary codes, from more basic items such as minimum distance and dimension to more complicated properties such as trellis decoding complexity and whether the Tanner graph of the code is cycle-free.
www.eccpage.com   (1019 words)

 [No title]   (Site not responding. Last check: 2007-11-02)
Consider the BCH code of Example 5 of Page 58 of Mackiw.
Using the code of the previous problem, take a valid codeword and change it by making three errors.
, determine the length of an RSA code you obtain from this field, and determine the degree of a generator polynomial needed to have 2048 codewords.
www.math.nmsu.edu /~pmorandi/math331s01/Assign9Solns.html   (495 words)

 BCH Code, 2005 Edition   (Site not responding. Last check: 2007-11-02)
This publication contains the Code for the Construction and Equipment of Ships Carrying Dangerous Chemicals in Bulk (BCH Code) and a number of documents closely related to that Code.
The Code was originally adopted in 1971 and was altered by a series of amendments between 1972 and 1983 before this amended version was adopted by the Marine Environment Protection Committee (MEPC) in 1985 and by the Maritime Safety Committee (MSC) in 1986.
There have been further amendments, the most recent of which were adopted by the MEPC by resolution MEPC.56(33) in October 1992 and by the MSC by the resolution MSC.29(61) in December 1992.
www.maritimetraining.com /itemdetail.asp?id=BIB772   (187 words)

 The Art of Error Correcting Coding: Cyclic codes and BCH codes   (Site not responding. Last check: 2007-11-02)
Encoding and decoding of a shortened cyclic code:
NOTE: For the BCH decoders below and the RS decoders in another section, log and antilog tables are used to solve equations for the unkown error positions (and values for RS codes).
Encoding and decoding of a shortened binary (48,36,5) BCH code:
the-art-of-ecc.com /3_Cyclic_BCH/index.html   (260 words)

 [No title]
// bch.cpp // // C++ code by Kevin Harmon and Leonid Reyzin (reyzin@cs.bu.edu) // for sublinear-time syndrome encoding and decoding of // binary BCH codes.
NTL_CLIENT /////////////////////////////////////////////////////////////////////////// // PURPOSE: // Computes the syndrome of a sparse vector // of the binary BCH code of design distance d.
170-173 of "Introduction to Coding Theory" by Jurgen Bierbrauer.
www.cs.bu.edu /~reyzin/code/bch.cpp   (446 words)

 BCH Encoder (Communications Blockset)   (Site not responding. Last check: 2007-11-02)
Create a BCH code from binary vector data
The BCH Encoder block creates a BCH code with message length K and codeword length N. You specify both N and K directly in the block mask.
For a given codeword length N, only specific message lengths K are valid for a BCH code.
www-rohan.sdsu.edu /doc/matlab/toolbox/commblks/ref/bchencoder.html   (179 words)

 The Merchant Shipping (BCH Code) (Amendment) Regulations 1990
These Regulations may be cited as the Merchant Shipping (BCH Code) (Amendment) Regulations 1990 and shall come into force on 1st January 1991.
Additional substances have been added to Chapters VI and VII of the BCH Code largely from pollution aspects and there has been some change in existing categorisation and some editorial amendment.
Copies of the Code and MARPOL Amendments are obtainable from the International Maritime Organization, 4 Albert Embankment, London SE1 7SR.
www.opsi.gov.uk /si/si1990/Uksi_19902603_en_1.htm   (701 words)

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