On cyclic codes over the ring $$\mathbb Z _p[u]/\langle u^k\rangle $$ Z p [ u ] / 〈 u k 〉

Cyclic codes over the ring Zp[u,v]/〈u2Kewat1, Ghosh2, Pattanayak3 2015Finite Fields and Their ApplicationsSelf Cite16030View full textAdd to dashboardCite

“…The structures of cyclic codes over rings have been discussed in a series of papers [1,2,[5][6][7][8][9]13,16,19]. The structures of cyclic codes of length n over a finite chain ring have been discussed in [11], when n is not divisible by the characteristic of the residue field R. The structures of cyclic codes of length n, where n is divisible by the characteristic of the residue field R, over some finite chain ring have been discussed in [3,4,10,17].…”

“…The authors of [12] have considered the more general ring F 2 [u 1 , u 2 , · · · , u k ]/ u 2 i , u 2 j , u i u j −u j u i , and studied the general properties of cyclic codes over these rings and characterized the nontrivial one-generator cyclic codes. Sobhani and Molakarimi in [18] extended these studies to cyclic codes over the ring…”

“…We also find the Hamming distance of these codes for length p l . Note that the rank and the Hamming distance of these cyclic codes for p = 2 have not been discussed in [12,18,20]. Hence getting the rank and the Hamming distance of the cyclic codes over R u 2 ,v 2 ,p is new even for p = 2.…”

“…The techniques we have used to find a set of generators are similar to those in [3,17]. Let C be a cyclic code over the ring R u 2 ,v 2 ,p .…”

“…Then we define the projection map from R u 2 ,v 2 ,p,n → R u 2 ,p,n and we get an ideal in the ring R u 2 ,p,n , which gives a cyclic code over the ring R u 2 ,p . The structure of cyclic codes over the ring R u 2 ,p is known from [17]. By pullback, we find a set of generators for a cyclic code over the ring R u 2 ,v 2 ,p .…”