A Large Class of p-Ary Cyclic Codes and Sequence Families

Zhengchun ZHOU  Xiaohu TANG  Udaya PARAMPALLI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A   No.11   pp.2272-2277
Publication Date: 2010/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.2272
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Signal Design and its Application in Communications)
Category: Sequences
cyclic code,  p-ary sequence,  quadratic form,  

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Let n,k,e,m be positive integers such that n≥ 3, 1 ≤ kn-1, gcd(n,k)=e, and m= is odd. In this paper, for an odd prime p, we derive a lower bound for the minimal distance of a large class of p-ary cyclic codes Cl with nonzeros α-1, α-(pk+1), α-(p3k+1), …, α-(p(2l-1)k+1), where 1 ≤ l ≤ and α is a primitive element of the finite field Fpn. Employing these codes, p-ary sequence families with a flexible tradeoff between low correlation and large size are constructed.