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Open AccessArticle

MDS Self-Dual Codes and Antiorthogonal Matrices over Galois Rings

School of Liberal Arts, KoreaTech, Cheonan 31253, Korea
Information 2019, 10(4), 153; https://doi.org/10.3390/info10040153
Received: 21 March 2019 / Revised: 15 April 2019 / Accepted: 24 April 2019 / Published: 25 April 2019
(This article belongs to the Section Information Theory and Methodology)
In this study, we explore maximum distance separable (MDS) self-dual codes over Galois rings G R ( p m , r ) with p 1 ( mod 4 ) and odd r. Using the building-up construction, we construct MDS self-dual codes of length four and eight over G R ( p m , 3 ) with ( p = 3 and m = 2 , 3 , 4 , 5 , 6 ), ( p = 7 and m = 2 , 3 ), ( p = 11 and m = 2 ), ( p = 19 and m = 2 ), ( p = 23 and m = 2 ), and ( p = 31 and m = 2 ). In the building-up construction, it is important to determine the existence of a square matrix U such that U U T = I , which is called an antiorthogonal matrix. We prove that there is no 2 × 2 antiorthogonal matrix over G R ( 2 m , r ) with m 2 and odd r. View Full-Text
Keywords: antiorthogonal matrices; Galois rings; MDS codes; self-dual codes antiorthogonal matrices; Galois rings; MDS codes; self-dual codes
MDPI and ACS Style

Han, S. MDS Self-Dual Codes and Antiorthogonal Matrices over Galois Rings. Information 2019, 10, 153.

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