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On generalized Hamming weights of BCH codes
IEEE Transactions on Information Theory, 1994A method is introduced to determine the generalized Hamming weights [\textit{V. K. Wei}, IEEE Trans. Inf. Theory 37, No. 5, 1412--1418 (1991; Zbl 0735.94008)] of certain families of codes, by the use of a geometric description of their dual. This method is ruled out by the authors to calculate some generalized weights of BCH(2) and BCH(3).
van der Geer, G.B.M., van der Vlugt, M.
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Sum-product decoding of BCH codes
2008 5th International Symposium on Turbo Codes and Related Topics, 2008This paper proposes methods to improve soft-input and soft-output decoding performance of BCH codes by sum-product algorithm (SPA). A method to remove cycles of length four (RmFC) in the Tanner graph has been proposed. However, the RmFC can not realize good decoding performance for BCH codes which have more than one error correcting capability.
Haruo Ogiwara +2 more
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IEEE Transactions on Information Theory, 2017
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Shuxing Li +3 more
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Shuxing Li +3 more
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Journal of Combinatorial Designs, 1997
Summary: We develop the theory of a generalization of the notion of BCH-code to additive codes, which are not necessarily linear. The usefulness of this notion is demonstrated by constructing a large number of record-breaking linear codes via concatenation.
Edel, Yves, Bierbrauer, Jürgen
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Summary: We develop the theory of a generalization of the notion of BCH-code to additive codes, which are not necessarily linear. The usefulness of this notion is demonstrated by constructing a large number of record-breaking linear codes via concatenation.
Edel, Yves, Bierbrauer, Jürgen
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1992
Abstract The polynomial corresponding to a word w will be denoted by w(x), using the same letter, indeed we shall eventually identify words and polynomials. The set of all binary polynomials of degree less than n will be denoted by Pn (P for polynomial, but note that the maximum degree is n -1).
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Abstract The polynomial corresponding to a word w will be denoted by w(x), using the same letter, indeed we shall eventually identify words and polynomials. The set of all binary polynomials of degree less than n will be denoted by Pn (P for polynomial, but note that the maximum degree is n -1).
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On subgroup subcodes of BCH codes
J. Inf. Process. Cybern., 1991Summary: An approach to multiple errors correcting \(q\)-ary codes, viewed as subgroup subcodes of BCH codes, is presented. It has been shown that in the case of \(d\leqq q=p^ l\) for an infinite sequence of lengths the cardinality of obtained codes exceeds the cardinality of the corresponding BCH codes not less than \((q/p)^{d-2}\) times, i.e.
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BCH Codes with Minimum Distance Proportional to Code Length
SIAM Journal on Discrete Mathematics, 2021Xiao-Nan Lu, Ying Miao
exaly