On a class of cyclic codes whose minimum distance exceeds the BCH bound

Abstract

It is shown that for any prime p and any integer ℓ ≥ 1, there is a cyclic code of length p^2(ℓ+1) - 1 and dimension p^ℓ+1(p^ℓ+1 - 2) over the finite field GF(p) whose minimum distance ≥ p + 2ℓ is greater than or equal to the BCH bound p + 2.