2018/01/14 by Supawadee Prugsapitak, Prugsapitak, Supawadee, Somphong Jitman +3 · 4 citations
Computer Science · Engineering · Mathematics · Social Sciences · #11N25 #94B15 #94B60 #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT) #Islamic Finance and Communication #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1801.04614
openalex publication_date 2018/01/14 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Good integers introduced in 1997 form an interesting family of integers that\nhas been continuously studied due to their rich number theoretical properties\nand wide applications. In this paper, we have focused on classes of\n2^\β-good integers, 2^\β-oddly-good integers, and\n2^\β-evenly-good integers which are generalizations of good integers.\nProperties of such integers have been given as well as their applications in\ncharacterizing and enumerating self-dual negacyclic codes over finite fields.\nAn alternative proof for the characterization of the existence of a self-dual\nnegacyclic code over finite fields has been given in terms of such generalized\ngood integers. A general enumeration formula for the number of self-dual\nnegacyclic codes of length n over finite fields has been established. For\nsome specific lengths, explicit formulas have been provided as well. Some known\nresults on self-dual negacyclic codes over finite fields can be formalized and\nviewed as special cases of this work.\n