Somphong Jitman
Department of Mathematics, Faculty of Science, Silpakorn University

16:00 Wednesday 1 March 2017, Room 3303, MUIC

God made the integers, all else is the work of man.
– L. Kronecker

A class of good integers has been introduced by P. Moree in 1997 together with the characterization of good odd integers. Such integers have been shown to have nice theoretical properties and wide applications. In this talk, a complete characterization of all good integers will be given. Two subclasses of good integers will be discussed, namely, oddly-good and evenly-good integers. As an application, good integers and oddly-good integers are applied in the study of some special families of cyclic/abelian codes.

1. Jia, Y., Ling, S., Xing, C., On self-dual cyclic codes over finite fields, IEEE Trans. Inform. Theory, 57, 2243–2251 (2011).
2. Jitman, S., Good integers and applications in coding theory, https://arxiv.org/abs/1611.04539, https://link.springer.com/article/10.1007/s12095-017-0255-4
3. Jitman, S., Ling, S., Liu, H., Xie, X., Abelian codes in principal ideal group algebras, IEEE Transactions on Information Theory, 59, 3046–3058 (2013).
4. Jitman, S., Ling, S., Sole, P., Hermitian self-dual abelian codes, IEEE Transactions on Information Theory, 60, 1496 –1507 (2014).