AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES

Title & Authors
AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES
Kim, Jon-Lark; Lee, Yoonjin;

Abstract
Self-dual codes have been actively studied because of their connections with other mathematical areas including t-designs, invariant theory, group theory, lattices, and modular forms. We presented the building-up construction for self-dual codes over GF(q) with $\small{q{\equiv}1}$ (mod 4), and over other certain rings (see [19], [20]). Since then, the existence of the building-up construction for the open case over GF(q) with $\small{q=p^r{\equiv}3}$ (mod 4) with an odd prime p satisfying $\small{p{\equiv}3}$ (mod 4) with r odd has not been solved. In this paper, we answer it positively by presenting the building-up construction explicitly. As examples, we present new optimal self-dual [16, 8, 7] codes over GF(7) and new self-dual codes over GF(7) with the best known parameters [24, 12, 9].
Keywords
building-up construction;linear codes;self-dual codes;
Language
English
Cited by
1.
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2.
t-CIS codes over GF(p) and orthogonal arrays, Discrete Applied Mathematics, 2017, 217, 601
3.
On the Problem of the Existence of a Square Matrix U Such That UUT=-I over Zpm, Information, 2017, 8, 3, 80
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