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

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