New Hermitian self-dual MDS or near-MDS codes over finite fields

joko Suprijanto^1,2, Yudi Renata² & MustikaLadia Putri²¹Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, InstitutTeknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia 
²Department of Mathematics,Faculty of Mathematics and Natural Sciences,
Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia  
Email: djoko@math.itb.ac.id

Abstract. A linear code over a finite field is called Hermitian self-dual if the code is self-dual under the Hermitian inner-product. The Hermitian self-dual code is called MDS or near-MDS if the code attains or almost attains the Singleton bound. In this paper we construct new Hermitian self-dual MDS or near-MDS codes over and of length up to 14. 

Keywords: decoding error probability performance; Hermitian self-dual codes; lexicographical ordering; MDS codes; near-MDS codes.