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

Djoko Suprijanto1,2, Yudi Renata2 & MustikaLadia Putri2
1Combinatorial 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.

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