Cyclic Codes from a Sequence over Finite Fields

  • Nopendri Nopendri Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung. Cybernetics Research Group, School of Industrial and System Engineering, Telkom University, Bandung. https://orcid.org/0000-0001-9641-677X
  • Intan Muchtadi-Alamsyah Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung https://orcid.org/0000-0001-7059-3196
  • Djoko Suprijanto Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung https://orcid.org/0000-0002-2836-9358
  • Aleams Barra Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung
Keywords: cyclic codes, sequences, linear span, cyclotomic coset, minimal polynomials

Abstract

A cyclic code has been one of the most active research topics in coding theory because they have many applications in data storage systems and communication systems. They have efficient encoding and decoding algorithms. This paper explains the construction of a family of cyclic codes from sequences generated by a trace of a monomial over finite fields of odd characteristics. The parameter and some examples of the codes are presented in this paper.
Published
2021-08-05
Section
Nonlinear Analysis