00000caa a22000003i 4500 UP-1685594773862388320 Buklod 20210309174224.0 m | | ta 210309s2017 xx r |||| u|eng d (iLib)UPBAG-00039458322 STII-DOST BAG rda eng ARTICLE-2532 Consorte, Odessa D. author. On Euclidean and Hermitian self-dual cyclic codes over GF(2r) by Odessa D. Consorte and Lilibeth D. Valdez. 2017. pages 129-136 26 cm text rdacontent unmediated rdamedia volume rdacarrier Includes bibliographical references (page 134) Jia et al. (2011) and Jitman et al. (2014) characterized Euclidean and Hermitian self-dual cyclic codes, respectively, by considering reciprocal and conjugate-reciprocal factors of the generator polynomial of these codes. In this paper, we give an alternative approach to this study by using splittings and cyclomatic cosets. We prove the existence of nontrivial Euclidean self-dual cyclic codes of length n = 2v · ñ, where ñ is odd, over GF (2r) in terms of the existence of a nontrivial splitting (Z, X0, X1) of Zñ by µ-1, where Z, X0, X1 are unions of 2r-cyclomatic cosets mod ñ. We express the formula for the number of cyclic self-dual codes over GF(2r) for each n and r in terms of the number of 2r-cyclomatic cosets in X0 (or in X1). In addition, we look at Hermitian self-dual cyclic codes. Nontrivial Hermitian self-dual codes over GF(22e) exist based on the existence of a nontrivial splitting (Z, X0, X1) of Zñ by µ-2e, where (Z, X0, X1) are unions of 22e-cyclomatic cosets mod ñ. From this splitting, we give a formula for the number of Hermitian self-dual cyclic codes for each n. Furthermore, we give an arithmetic condition on the length n such that nontrivial Hermitian self-dual cyclic codes exist. (Author's abstract) Mathematics. Cyclic codes. Cyclotomic cosets. Euclidian dual. Hermitian dual. Self-dual codes. Splittings. Valdez, Lilibeth D. author. The Philippine Journal of Science Vol. 146, no. 2, June 2017. Request full-text access via UPB University Library through https://forms.gle/KZjBv7aRtY6jiL5E9 (viewed 09 March 2021) FI UPBAG UPBAG-MAIN ARTICLE-2532 Analytics