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

Abstract

Let n, k, e, m be positive integers such that n ≥ 3, 1 ≤ k ≤ n - 1, gcd(n, k) = e, and $m={n\\over e}$ 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-(pk+1), α-(p3k+1), …, α-(p(2l-1)k+1), where $1\\leq l\\leq {m-1\\over 2}$ 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.