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 … 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 …
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 …
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 … 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.
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 … 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 …
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 …
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 ... csi crate and burialWebNov 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 … eagle cliff trail nhWebZhou 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. eaglecliff trustpilotWebAbsolute 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 … eagle cliffs billings mtWebhave 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. eagle climbing fitnessWebIn 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. … eagle climbing + fitnessWebThe 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. csic red social