English

On cyclotomic cosets and code constructions

Information Theory 2016-01-01 v1 Combinatorics math.IT

Abstract

New properties of qq-ary cyclotomic cosets modulo n=qm1n = q^{m} - 1, where q3q \geq 3 is a prime power, are investigated in this paper. Based on these properties, the dimension as well as bounds for the designed distance of some families of classical cyclic codes can be computed. As an application, new families of nonbinary Calderbank-Shor-Steane (CSS) quantum codes as well as new families of convolutional codes are constructed in this work. These new CSS codes have parameters better than the ones available in the literature. The convolutional codes constructed here have free distance greater than the ones available in the literature.

Keywords

Cite

@article{arxiv.1511.04359,
  title  = {On cyclotomic cosets and code constructions},
  author = {Giuliano Gadioli La Guardia and Marcelo Muniz Silva Alves},
  journal= {arXiv preprint arXiv:1511.04359},
  year   = {2016}
}

Comments

Accepted for publication in Linear Algebra and its Applications

R2 v1 2026-06-22T11:44:41.784Z