Binary primitive lcd bch codes

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August undefined, 2024

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. 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 …

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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 … 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 … east grand forks sanford clinic

BCH code - Wikipedia

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. WebNov 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 … 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 ... culligan water mokena il

Parameters of LCD BCH codes with two lengths Request PDF

Dimension of nonbinary antiprimitive BCH codes DeepAI

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 … 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. … culligan water monmouth ilWebDec 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. culligan water moncton

"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 ... " - Binary primitive lcd bch codes

Binary primitive lcd bch codes

[2104.04193] Ternary primitive LCD BCH codes - arXiv.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 ... 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 …

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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. http://souktha.github.io/misc/bch15_7_5/

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 … WebFurthermore, we mainly focus on the primitive q-ary BCH codes C ( q , n , δ , b ) when b = 0 and b = 1 based on the general characterization. ... The weight distributions of extended binary primitive BCH codes of length 128, ... Binary LCD codes and self-orthogonal codes from a generic construction, IEEE Trans. Inf. Theory 65 (1) (2024) 16 ...

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 … 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 …

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 …

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 … culligan water moses lakeWebZhou 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. culligan water morro bay caWebDec 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 … culligan water moscow idahoWebJul 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 ... east grand forks soccerWebA 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. east grand forks senior center menuWebSep 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; culligan water morehead city ncWebFor 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 … east grand forks senior high staff directory