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Construction of new linear codes with good parameters from group rings and skew group rings

Year: 2024
Type: article
Abstract: In this paper, we use the left principal ideals of group rings and skew group rings to construct linear codes over small finite fields. We study three class of groups: Semidirect product of two cyclic groups, direct product of a cyclic group and semidirect product of two cyclic groups, wreath product of a cyclic group of order n and a cyclic group of order 2. Using these groups, we can get some generator matrices over F q . Then by computer search, we obtain 18 new linear codes with parameters [ 32 , 19 , 8 ] 3 , [ 36 , 22 , 8 ] 3 , [ 39 , 21 , 10 ] 3 , [ 40 , 26 , 8 ] 3 , [ 40 , 30 , 6 ] 3 , [ 55 , 16 , 22 ] 3 , [ 40 , 8 , 24 ] 4 , [ 40 , 11 , 20 ] 4 , [ 40 , 27 , 8 ] 4 , [ 42 , 29 , 8 ] 4 , [ 42 , 25 , 10 ] 4 , [ 50 , 13 , 24 ] 4 , [ 50 , 9 , 30 ] 5 , [ 39 , 12 , 19 ] 5 , [ 40 , 8 , 26 ] 7 , [ 18 , 12 , 6 ] 9 , [ 21 , 16 , 5 ] 9 , [ 42 , 7 , 30 ] 9 .
DOI: 10.1016/j.disc.2024.114349
Language: English
Open Access status: hybrid
Estimated APC paid: $3,120
OpenAlex ID: W4405290394
FWCI: 0.148
Cites: 14
Cited by: 1
Related to: 10