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

TL;DR

This paper introduces a new polynomial-time bound for cyclic codes that generalizes existing bounds like Hartmann-Tzeng and Betti-Sala, often providing the tightest estimates for code distance.

Contribution

The authors develop a unified algebraic reformulation of classical bounds and propose a new generalized bound with polynomial complexity, improving code distance estimation.

Findings

The new bound is often the tightest among polynomial-time bounds.

It generalizes the Hartmann-Tzeng and Betti-Sala bounds.

The bound has polynomial computational complexity.

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.