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Binary codes from Paley graphs of prime-power-square order
- 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.
- Subjects :
- Discrete mathematics
Paley graph
Partial permutation
020206 networking & telecommunications
0102 computer and information sciences
02 engineering and technology
01 natural sciences
Prime (order theory)
Square (algebra)
Theoretical Computer Science
Combinatorics
010201 computation theory & mathematics
0202 electrical engineering, electronic engineering, information engineering
Discrete Mathematics and Combinatorics
Binary code
Adjacency matrix
Prime power
Decoding methods
Mathematics
Subjects
Details
- ISSN :
- 0012365X
- Volume :
- 342
- Database :
- OpenAIRE
- Journal :
- Discrete Mathematics
- Accession number :
- edsair.doi...........732ae438fadc00e410ef465eecede391