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Binary primitive lcd bch codes

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. 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.

Blind recognition of binary BCH codes based on Euclidean algorithm

WebSep 3, 2024 · Comparing coset leaders, we introduce the new concept of absolute coset leaders, which provides advantages for constructing LCD BCH codes. We then give explicit presentations for the largest, second largest and third largest absolute coset leaders … WebApr 9, 2024 · Absolute coset leaders were first proposed by the authors which have 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. canfield ohio flower shop https://flowingrivermartialart.com

On LCD codes and lattices Request PDF - ResearchGate

WebZhou et al. [28] obtained optimal or almost optimal binary LCD codes by using a generic construction. Liu et al. [16] discussed the dimension of some binary LCD BCH codes of length 2 m + 1. WebSep 1, 2024 · A novel method based on Euclidean algorithm is proposed to solve the problem of blind recognition of binary Bose–Chaudhuri–Hocquenghem (BCH) codes in non-cooperative applications. By carrying out iterative Euclidean divisions on the demodulator output bit-stream, the proposed method can determine the codeword length … WebJul 1, 2016 · We describe binary and ternary LCD codes constructed as subfield-subcodes of $J$-affine variety codes and provide some new and good LCD codes coming from … fitbit advertisement car wrap

Blind recognition of binary BCH codes based on Euclidean algorithm

Category:Dimension of nonbinary antiprimitive BCH codes DeepAI

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Binary primitive lcd bch codes

Ternary Primitive LCD BCH codes - aimsciences.org

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. … Web2454 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 …

Binary primitive lcd bch codes

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WebJan 1, 2024 · Abstract. In this paper, we study LCD BCH codes over the finite field GF (q) with two types of lengths n, where n = ql + 1 and n = (ql + 1)/ (q + 1). Several classes of LCD BCH codes are given and ... 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 …

WebNov 8, 2024 · Especially for binary primitive narrow-sense BCH codes, the new bounds on the minimum distances of the dual codes improve the classical Sidel’nikov bound, and … 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 ...

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 … WebApr 9, 2024 · Ternary primitive LCD BCH codes Xinmei Huang, Qin Yue, Yansheng Wu, Xiaoping Shi Absolute coset leaders were first proposed by the authors which have …

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 …

WebDec 19, 2024 · Ternary primitive LCD BCH codes ... The binary BCH codes were introduced independently by Hocquenghem in 1959 Hocquenghem and by Bose and Ray-Chaudhuri in 1960 Bose1 Bose2 . Immediately afterwards Gorenstein and Zierler generalized binary BCH codes to all finite fields. Since then, BCH codes have been … fitbit age restrictionWebDec 21, 2024 · Bose-Chaudhuri-Hocquenghem (BCH) codes have been intensively investigated. Even so, there is only a little known about primitive BCH codes, let alone non-primitive ones. fitbit afib newsWebThe generator polynomial of the BCH code is defined as the least common multiple g(x) = lcm (m1(x),…,md − 1(x)) . It can be seen that g(x) is a polynomial with coefficients in GF … fitbit air conditionerWebDec 1, 2024 · Binary primitive LCD BCH codes Xinmei Huang 1,2 · Qin Yue 2,3 · Yansheng Wu 4 · Xiaoping Shi 5 · Jerod Michel 6 Received: 7 April 2024 / Revised: 10 … fitbit alarm appWebLi 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 … fitbit alarm clockWebLi 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 … fitbit age rangeWebMar 7, 2024 · A BCH code of length n over Fq is always relative to an n-th primitive root of unity β in an extension field of Fq, and is called a dually-BCH code if its dual is also a BCH code relative to the ... fitbit aktionscode