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Binary codes from Paley graphs of prime-power-square order

Authors :
Jirapha Limbupasiriporn
Source :
Discrete Mathematics. 342:111588
Publication Year :
2019
Publisher :
Elsevier BV, 2019.

Abstract

We examine the binary code from the row span of an adjacency matrix of the Paley graph of order q 2 , where q is a prime power such that q 2 ≡ 1 ( mod 8 ) . We show that the code and its dual are respectively [ q 2 , q 2 − 1 2 , q + 1 ] 2 and [ q 2 , q 2 + 1 2 , q ] 2 codes. We obtain spanning sets of minimum-weight vectors for these codes, and in the case of q a prime we show that the code can be used for partial permutation decoding using a certain information set.

Details

ISSN :
0012365X
Volume :
342
Database :
OpenAIRE
Journal :
Discrete Mathematics
Accession number :
edsair.doi...........732ae438fadc00e410ef465eecede391