首页|Ternary isodual codes and 3-designs

Ternary isodual codes and 3-designs

扫码查看
原文链接
  • NETL
  • NSTL
Ternary isodual codes and their duals are shown to support 3-designs under mild symmetry conditions. These designs are held invariant by a double cover of the permutation part of the automorphism group of the code. Examples of interest include extended quadratic residues (QR) codes of lengths 14 and 38 whose automorphism groups are PSL(2, 13) and PSL(2, 37), respectively. We also consider Generalized Quadratic Residue (GQR) codes in the sense of Lint and MacWiliams (IEEE Trans Inf Theory 24(6): 730-737,1978). These codes are the abelian generalizations of the Quadratic Residue (QR) codes which are cyclic. We construct them as row span of a Jacobsthal matrix. In lengths 50 and 26 we obtain 3-designs invariant under a double cover of PΣL(2,49), and PΣL(2, 25), respectively. In addition, from block orbits of these 3-designs we construct a number of other 3-designs and 2-designs. Finally, we apply the same construction to the binary extended GQR code of length 82.

Abelian codesGQR codesternary codesPΣL(2q)3-designs

Minjia Shi、Ruowen Liu、Dean Crnkovic、Patrick Sole、Andrea Svob

展开 >

Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei 230601, China||State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China

Faculty of Mathematics, University of Rijeka, Rijeka, Croatia

CNRS, I2M, Aix Marseille Univ, Marseilles, France

2025

10.1007/s10623-024-01558-9

Designs, codes and cryptography

Designs, codes and cryptography

ISSN：0925-1022
年,卷(期)：2025.93(6)