Journal article
A large class of p-ary cyclic codes and sequence families
Z Zhou, X Tang, U Parampalli
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences | IEICE-INST ELECTRONICS INFORMATION COMMUNICATIONS ENG | Published : 2010
Abstract
Let n, κ, e,m be positive integers such that n ≤ 3, 1 ≤ κ ≤ n - 1, gcd(n, κ) = e, and m = n/e 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-(pκ+1)α-(p3κ+1), ⋯ , α-(p(2l-1)κ+1), where 1 ≤ l ≤ m-1/2 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. Copyright © 2010.
Grants
Awarded by National Science Foundation of China (NSFC)
Awarded by Southwest Jiaotong University
Awarded by Fundamental Research Funds for the Central Universities
Funding Acknowledgements
The work of Z Zhou and X Tang was supported in part by the National Science Foundation of China (NSFC) under Grant 60772086 the Doctors Innovation Funds of Southwest Jiaotong University, 2009 the Funds for the Excellent PH D Dissertation of Southwest Jiaotong University under Grant A0310119950101-6, and the Fundamental Research Funds for the Central Universities under Grants SWJTU09BR201 and SWJTU09ZT37 The work of P Udaya was in part supported by Melbourne Research Grant Scheme 2009 of University of Melbourne