A generalization of bounds for cyclic codes, including the HT and BS bounds

We use the algebraic structure of cyclic codes and some properties of the discrete Fourier transform to give a reformulation of several classical bounds for the distance of cyclic codes, by extending techniques of linear algebra. We propose a bound, whose computational complexity is polynomial bounded, which is a generalization of the Hartmann-Tzeng bound and the Betti-Sala bound. In the majority of computed cases, our bound is the tightest among all known polynomial-time bounds, including the Roos bound

Generalizations of the BCH bound

Cyclic codes generated by polynomials having multiple sets of do — 1 roots in consecutive powers of a nonzero field element are considered and some generalizations of the BCH bound are presented. In particular, it is shown, among other results, that if g(x) GF(q)[x[ is the generator polynomial of a cyclic code Vn of length n such that g(βl+i1c1+i2c2 = 0 for i1 = 0, 1,…, d0 — 2 and i2 = 0,1,…,s, where β GF(qm) is a nonzero element of order n and c1 , c2 are relatively prime to n, then the minimum distance of Vn is at least d0 + s