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Quadratic residue codes, rank three groups and PBIBDs
- Source :
- Designs, Codes and Cryptography, Designs, Codes and Cryptography, Springer Verlag, 2021, Designs, Codes and Cryptography, 2021
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- The automorphism group of the Zetterberg code Z of length 17 (also a quadratic residue code) is a rank three group whose orbits on the coordinate pairs determine two strongly regular graphs equivalent to the Paley graph attached to the prime 17. As a consequence, codewords of a given weight of Z are the characteristic vectors of the blocks of a PBIBD with two associate classes of cyclic type. More generally, this construction of PBIBDs is extended to quadratic residue codes of length $$\equiv 1 \pmod {8},$$ to the adjacency codes of triangular and lattice graphs, and to the adjacency codes of various rank three graphs. A remarkable fact is the existence of 2-designs held by the quadratic residue code of length 41 for code weights 9 and 10.
- Subjects :
- Strongly regular graph
cyclic codes
Paley graph
Applied Mathematics
Strongly Regular Graphs
Lattice (group)
020206 networking & telecommunications
0102 computer and information sciences
02 engineering and technology
Quadratic residue code
Type (model theory)
01 natural sciences
Computer Science Applications
Combinatorics
Quadratic residue
Rank three groups
[INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT]
010201 computation theory & mathematics
0202 electrical engineering, electronic engineering, information engineering
Adjacency list
Rank (graph theory)
Mathematics
Subjects
Details
- ISSN :
- 15737586 and 09251022
- Volume :
- 90
- Database :
- OpenAIRE
- Journal :
- Designs, Codes and Cryptography
- Accession number :
- edsair.doi.dedup.....4b934ff046a69da49472cc90935defe6