Geodesic
Duadic codes over Fp + uFp + vFp + uvFp
Filomat, Tome 37 (2023) no. 12, p. 3985

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

Duadic codes constitute a well-known class of cyclic codes. In this paper, we study the structure of duadic codes of length n over the ring R = F p + uF p + vF p + uvF p , u 2 = v 2 = 0, uv = vu, where p is prime and (n, p) = 1. These codes have been studied here in the setting of abelian codes over R, and we have used Fourier transform and idempotents to study them. We have characterized abelian codes over R by studying their torsion and residue codes. It is shown that the Gray image of an abelian code of length n over R is a binary abelian code of length 4n. Conditions for self-duality and self-orthogonality of duadic codes over R are derived. Some conditions on the existence of self-dual augmented and extended codes over R are presented. We have also studied Type II self-dual augmented and extended codes over R. Some results related to the minimum Lee distances of duadic codes over R are presented. We have also presented a sufficient condition for abelian codes of the same length over R to have the same minimum Hamming distance. Some optimal binary linear codes of length 36 and ternary linear codes of length 16 have been obtained as Gray images of duadic codes of length 9 and 4, respectively, over R using the computational algebra system Magma.
DOI : 10.2298/FIL2312985K
Classification : 94B05, 94B15
Keywords: Abelian codes, duadic codes, self-dual codes 
Raj Kumar; Mahesha; and Bhaintwal. Duadic codes over Fp + uFp + vFp + uvFp. Filomat, Tome 37 (2023) no. 12, p. 3985 . doi: 10.2298/FIL2312985K
@article{10_2298_FIL2312985K,
     author = {Raj Kumar and Mahesha and and Bhaintwal},
     title = {Duadic codes over {Fp} + {uFp} + {vFp} + {uvFp}},
     journal = {Filomat},
     pages = {3985 },
     year = {2023},
     volume = {37},
     number = {12},
     doi = {10.2298/FIL2312985K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2312985K/}
}
TY  - JOUR
AU  - Raj Kumar
AU  - Mahesha
AU  - and Bhaintwal
TI  - Duadic codes over Fp + uFp + vFp + uvFp
JO  - Filomat
PY  - 2023
SP  - 3985 
VL  - 37
IS  - 12
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2312985K/
DO  - 10.2298/FIL2312985K
LA  - en
ID  - 10_2298_FIL2312985K
ER  - 
%0 Journal Article
%A Raj Kumar
%A Mahesha
%A and Bhaintwal
%T Duadic codes over Fp + uFp + vFp + uvFp
%J Filomat
%D 2023
%P 3985 
%V 37
%N 12
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2312985K/
%R 10.2298/FIL2312985K
%G en
%F 10_2298_FIL2312985K

Cité par Sources :