Binary primitive lcd bch codes
WebJan 1, 2013 · Steane firstly proved that a binary primitive narrow-sense (NS) BCH code of length n = 2 m − 1 is Euclidean dual-containing if and only if its designed distance δ ≤ 2 m 2 −1 [7], whereafter ... WebFor a t-error correcting code, the generator polynomial Q(x) of standard BCH codes has the form Q(x) = p(x)p3(x)p5(x) p2t 1(x) (3) where p(x) is a primitve polynomial and all the …
Binary primitive lcd bch codes
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WebIn this paper, we explore two special families of LCD cyclic codes, which are both BCH codes. The dimensions and the minimum distances of these LCD BCH codes are … WebNov 2, 2024 · A pair of linear codes (C, D) of length n over $$\\mathbb {F}_q$$ F q is called a linear complementary pair (LCP) if their direct sum yields the full space $$\\mathbb {F}_q^n$$ F q n . By a result of Carlet et al. (2024), the best security parameters of binary LCPs of codes are left open. Motivated by this, we study binary LCPs of codes. We …
WebThe (Euclidean) hull of a linear code is defined to be the intersection of the code and its Euclidean dual. It is clear that the hulls are self-orthogonal codes, which are an important type of linear codes due to their wide applications in communication and cryptography. Let C ( 2, n, δ) be the binary primitive narrow-sense BCH code, where n ... Webhave advantages in constructing binary LCD BCH codes. As a continue work, in this paper we focus on ternary linear codes. Firstly, we find the largest, second largest, and third largest absolute coset leaders of ternary primitive BCH codes. Secondly, we present three classes of ternary primitive BCH codes and determine their weight distributions.
WebJul 15, 2024 · The binary primitive BCH codes are cyclic and are constructed by choosing a subset of the cyclotomic cosets. Which subset is chosen determines the dimension, the … WebIn this paper, we consider narrow-sense BCH codes of length n = q m − 1 N with designed distance δ = s q − 1 n proportional to n, where N divides q m − 1 q − 1 and 1 ≤ s ≤ q − 1. …
WebApr 9, 2024 · Secondly, we present three classes of ternary primitive BCH codes and determine their weight distributions. Finally, we obtain some LCD BCH codes and …
WebA t-error-correcting binary BCH code is capable of correcting any combination of t or fewer errors in a block of n = 2m-1 digits. For any positive integer m ≥3 and t < 2m-1, there exists a binary BCH code with the following parameters: Block length: n = 2m - 1 Number of information bits: k≥ n-m*t Minimum distance: d min ≥ 2t + 1. ri grupo sbfWebSep 3, 2024 · Binary primitive LCD BCH codes Authors (first, second and last of 5) Xinmei Huang; Qin Yue; Jerod Michel; Content type: OriginalPaper Published: 03 September 2024; Pages: 2453 - 2473; Optimal minimal linear codes from posets Authors (first, second and last of 4) Jong Yoon Hyun; rig service jraWebSep 6, 2024 · A code C is a linear complementary dual (LCD) code if \(C\cap C^\perp =\{0\}\).LCD codes were introduced by Massey [] and gave an optimum linear coding solution for the two user binary adder channel.The classification of LCD [n, k] codes and determination of the largest minimum weight among all LCD [n, k] codes are … rigsar projectrigs blue jeansWebLi S Li C Ding C Liu H Two families of LCD BCH codes IEEE Trans. Inf. Theory 2024 63 9 5699 5717 36880551374.94845 Google Scholar Digital Library 14. Li C Wu P Liu F On … ri grupo somaWebJul 1, 2016 · Binary primitive LCD BCH codes. December 2024 · Designs Codes and Cryptography. ... third largest absolute coset leaders and use them to construct binary LCD BCH codes. Lastly, we determine the ... ri grupo serWeb2454 X.Huangetal. Fq[x]/ xn −1 isaprincipleidealringandC isgeneratedbyamonicdivisor g(x)of xn −1. Here g(x) is called the generator polynomial of the code C, and we write =g(x). Let Zn ={0,1,...,n − 1} be the ring of integers modulo n.Fors ∈ Zn, assume that ls is the smallest positive integer such that sqls ≡ s (mod n).Then the q-cyclotomic coset containing s is … ri gu-1338