Binary primitive lcd bch codes
WebThe 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 … Webcorrecting code can be any primitive polynomial, say of degree r. A primitive polynomial is a prime (non-factorable) polynomial such that every polynomial of ... for simplicity, restrict to the binary eld and study binary BCH codes. 1 The BCH Code Denote messages, generators (encoding polynomials), codewords, and received mes-
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 ... WebLi 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 …
WebSep 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; 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 …
WebSep 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 … WebThe BCH Encoder block creates a BCH code with message length K and codeword length ( N – number of punctures). If the encoder is processing multiple codewords per frame, then the same puncture pattern holds for all codewords. The input and output signal lengths are listed in Input and Output Signal Length in BCH Blocks.
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 …
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 … onwardmobility公司WebAbsolute 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. Secondly, we present three classes of ternary … onward mfg huntington inWebDec 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 … onwardmobility blackberry いつ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. onwardmobility blackberry 5gWebSep 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 … onwardmobility.comWebNov 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 … onwardmobility stockWebIn 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. … iotlearner.com