Binary primitive lcd bch codes

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August undefined, 2024

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 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 …

Two Families of LCD BCH Codes IEEE Journals & Magazine - IEEE …

WebDec 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 … WebMar 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 ... barberini hotel roma

Ternary Primitive LCD BCH codes - aimsciences.org

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. 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. 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 ... barberini maler

Binary primitive LCD BCH codes Designs, Codes and …

Binary primitive LCD BCH codes SpringerLink

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. WebBuild on my earlier blog of a Hamming cyclic code of ( n, k, d) = ( 15, 11, 3), I will expand its capability to a binary BCH ( 15, 7, 5), t = 2 code based on the same primitive … supreme juice barWeb2454 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 … supreme jumper uk

"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 … " - Binary primitive lcd bch codes

Binary primitive lcd bch codes

Ternary Primitive LCD BCH codes - aimsciences.org

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 ... WebLCD codes for all parameters. In [24], Zhou et al. proposed some binary LCD codes and self-orthogonal codes. In this paper, we will always assume that n = 2m −1andthatα is a …

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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 minimum distance and the weight distribution of the BCH code. We construct possible BCH codes and determine their coderate, true minimum distance and the non-equivalent … 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-

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 … 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 …

WebThe encoding circuit for BCH codes is a binary division circuit while for Reed-Solomon codes, the division circuit is defined over 𝐺𝐹2𝑚, where 𝑚 is the size of the symbol. The addition in the BCH encoder as shown in Fig (a) is binary ‘XOR’ while the addition in the RS encoder in Fig(b) is addition over 𝐺𝐹2𝑚. WebTernary Primitive LCD BCH codes Xinmei Huang 1,2 , Qin Yue 3 , Yansheng Wu 4 and Xiaoping Shi 5 1. Department of Mathematics, Jinling Institute of Technology, Nanjing, …

WebJul 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 ... barberini lensesWebLi 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 … barberini massaggihttp://souktha.github.io/misc/bch15_7_5/ supreme justice borkWebThe 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. barberini maffeoWebLi 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 … barberini lenti sedeWebNov 30, 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. Secondly, we present three … supreme justice cavanaughWebJan 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 ... barberini mithraeum