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

Abstract

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.