Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 1
ON THE LINEAR CODES OVER THE RING Z4 + v1Z4 + ::: + vtZ4
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 809–823
- DOI
- —
Abstract
Some results on linear codes over the ring Z4 + uZ4 + vZ4; u2 =u; v2 = v; uv = vu = 0 in [6,7] are generalized to the ring Dt = Z4 + v1Z4 +::: + vtZ4; v2i = vi; vivj = vjvi = 0 for i 6= j; 1 i; j t. A Gray map tfrom Dntto Z(t+1)n4is deÖned. The Gray images of the cyclic, constacyclicand quasi-cyclic codes over Dt are determined. The cyclic DNA codes over Dtare introduced. The binary images of them are determined. The nontrivialautomorphism on Di for i = 2; 3; :::; t is given. The skew cyclic, skew constacyclic and skew quasi-cyclic codes over Dt are introduced. The Gray imagesof them are determined. The skew cyclic DNA codes over Dt are introduced.Moreover, some properties of MDS codes over Dt are discussed.