The q-ary antiprimitive bch codes
WebbMentioning: 10 - Artin-Schreier curves and codes - Geer, Gerard van der, Vlugt, Marcel van der Given a prime number q and prime power q with positive integers m and d such that d ≤ q − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q − 1 and distance at least d is constructed by the following method. Let α be a primitive element of GF(q ). For any positive integer i, let mi(x) be the minimal polynomial with coefficients in GF(q) of α . The generator polynomial of the BCH code is defined as the least …
The q-ary antiprimitive bch codes
Did you know?
WebbIn this paper, we will employ the defining set of the code C to present a general characterization when its hull has dimension k − ℓ. Furthermore, we mainly focus on the … WebbThe objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. Some lower bounds on the minimum distance of antiprimitive BCH …
Webb28 sep. 2024 · The objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. Some lower bounds on the minimum distance of … http://www.cim.nankai.edu.cn/xsbg/list4.htm
WebbBCH codes are called narrow-sense when b = 1, and are called primitive when n = 2 r − 1 for some r ≥ 2. The code dimension is related to the multiplicative order of 2 modulo n, i.e., … Webb28 sep. 2024 · The q-ary antiprimitive BCH codes Optimal bounds on codes for location in circulant graphs. Ville Junnila, et al. Some binary BCH codes with length n=2^m+1. …
WebbDetermining the dimensions of BCH codes is a challenging problem in coding theory. In this paper, we study BCH codes of length q m + 1 2, for odd m and m ≡ 2 ( mod 4). The first few largest coset leaders of such BCH codes are obtained. On the basis of this, we determine their parameters and obtain a few optimal or almost optimal codes.
Webb21 dec. 2024 · After deriving the cardinalities of the coset leaders, we shall calculate exact dimensions of many antiprimitive LCD BCH codes. PDF Abstract. Code Edit Add Remove … dickinson nd addressesWebb30 mars 2024 · BCH codes over GF (q) with length qm+1. CoRR abs/2106.11607 ( 2024) [i5] Hongwei Zhu, Minjia Shi, Xiaoqiang Wang, Tor Helleseth: The $q$-ary antiprimitive BCH codes. CoRR abs/2109.13803 ( 2024) 2024 [j13] abs/1910.05461 ( 2024) [i1] Dabin Zheng, Qing Zhao, Xiaoqiang Wang: Several classes of two-weight and three-weight linear codes. citrix freezes windows 11Webb17 feb. 2024 · 【学术报告】 施敏加 教授：The q-ary antiprimitive BCH codes. 2024-11-19. 每页 14 记录 总共 390 记录 ; dickinson nd accountantsWebbThe $q$-ary antiprimitive BCH codes Zhu, Hongwei ; Shi, Minjia ; Wang, Xiaoqiang ; Helleseth, Tor It is well-known that cyclic codes have efficient encoding and decoding … dickinson nd arrest recordsWebb30 nov. 2024 · The objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. Some lower bounds on the minimum distance of … dickinson nd apts for rentWebb1 jan. 2024 · Download Citation On Jan 1, 2024, Jiayuan Zhang and others published Some results on BCH codes of length $ \frac{{{q^m} + 1}}{2} Find, read and cite all the research you need on ResearchGate dickinson nd attorneysWebb3 juni 2024 · be characterized by the cyclotomic cosets. Let j[i] = fiqz mod njz 2Zgdenote the q-ary cyclotomic coset of i modulo n. Definition 2. A BCH code C over Fq with length n and designed distance d is a cyclic code. The defining set is denoted by Z = b+d 2 U i=b j[i]. If n = qm0 1, it is called a primitive BCH code. If dickinson nd arrests