Web20 de jul. de 1996 · The BCH code of length 1023 and designed distance 253 has minimum distance 253. The cyclic codes of length 2 11 Gamma 1; 2 13 Gamma 1; 2 17 Gamma 1, with generator polynomial m 1 (x) and m 7 (x ... Web15 de mar. de 2024 · In this paper, we provide two complementary results for cyclic codes of composite length. First, we give a general construction of cyclic codes of length nr …
On the minimum distance of cyclic codes - IEEE Xplore
WebSection 4 focuses on lower bounds for the minimum sum-rank distance of a cyclic-skew-cyclic code. We provide the analogues of the Roos bound and of the Hartmann-Tzeng bound, exploiting the notion of defining sets for cyclic-skew-cyclic codes. In Section 5 we focus on tensor products of codes. We combine a cyclic code in the Hamming Web2 de mai. de 2024 · 2. My goal is to find a generator polynomial for a binary [ 15, 5, d] cyclic code that corrects all errors with weight less than or equal to 3. I have to find a degree 10 monic polynomial that divides x 15 − 1 ( mod 2) and has weight 7. If 15 and 5 were coprime I would know how to factor x 15 − 1 using cyclotomic theory. tryphoera sunnyvale ca
Optimal cyclic quaternary constant‐weight codes of weight three
Web30 de jun. de 2014 · And we also calculate the minimum distance of some cyclic codes and give lower bounds on the minimum distance for some other cyclic codes. Keywords: Cyclic codes, Whiteman generalized cyclotomic sequences, generator polynomial, minimum distance. Mathematics Subject Classification: Primary: 58F15, 58F17; … WebAbstract: The minimum distance of a class of reversible cyclic codes has been proved to be greater than that given by the BCH bound. It is also noted that this class of codes … Web10 de mai. de 2011 · A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound … phillip island nature park austrália