Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH bound
<|reference_start|>Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH bound: In this paper we study the family of cyclic codes such that its minimum distance reaches the maximum of its BCH bounds. We also show a way to construct cyclic codes with that property by means of computations of some divisors of a polynomial of the form X^n-1. We apply our results to the study of those BCH codes C, with designed distance delta, that have minimum distance d(C)= delta. Finally, we present some examples of new binary BCH codes satisfying that condition. To do this, we make use of two related tools: the discrete Fourier transform and the notion of apparent distance of a code, originally defined for multivariate abelian codes.<|reference_end|>
@article{bernal2024cyclic,
    title={Cyclic and BCH Codes whose Minimum Distance Equals their Maximum BCH
  bound},
    author={Jos'e Joaqu'in Bernal, Diana H. Bueno-Carre~no and Juan Jacobo
  Sim'on},
    journal={arXiv preprint arXiv:2402.03965},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.03965},
    primaryClass={cs.IT math.IT}
}