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Binary primitive lcd bch codes

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 ... 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 …

Binary primitive LCD BCH codes SpringerLink

WebDec 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. 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. cypern februari https://scrsav.com

Dimension of nonbinary antiprimitive BCH codes DeepAI

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 … 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 … 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 … bim smith railing

Binary BCH (15,7,5) work out Soukthavy Sopha

Category:Ternary Primitive LCD BCH codes - aimsciences.org

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Binary primitive lcd bch codes

BCH code - Wikipedia

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; 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 …

Binary primitive lcd bch codes

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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. 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 …

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 ...

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 … 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.

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 …

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 … bims normal scoreWebBuild 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 … bimsmith revit familyhttp://souktha.github.io/misc/bch15_7_5/ bims numberWebApr 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 … cypern fotbollWebThe 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. cypern historieWebZhou 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. bims of 10 meansWebJan 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 ... cypern historia