Cyclic and some constacyclic codes over the ring Z4[u]〈u2<

On constacyclic codes over Z4[u]/〈u2

“…A lot of work for this has been done in recent years (e.g. [1,7,8,10,11,12]). For example, Wu et al discussed 1-generator generalized quasi-cyclic codes over Z 4 in [10].…”

“…The construction of one-Gray weight and two-Gray weight codes over Z 4 +uZ 4 with u 2 = u was studied in [8]. It is worth noting thatÖzen et al have proved that the Z 4 -image of a (2 + u)-constacyclic code over Z 4 +uZ 4 (u 2 = 1) of odd length is a cyclic code over Z 4 in [7]. They also presented many examples of cyclic codes over Z 4 + uZ 4 whose Z 4 -images have better parameters than previously best-known Z 4 -linear codes.…”

“…They also presented many examples of cyclic codes over Z 4 + uZ 4 whose Z 4 -images have better parameters than previously best-known Z 4 -linear codes. Checking the parameters of the new codes presented in [7], we noted that the entries in Table 1 of [7] are erroneous. One of the authors of [7] (who is also a co-author of this paper) confirmed that somehow incorrect data was entered into Table 1.…”

“…Checking the parameters of the new codes presented in [7], we noted that the entries in Table 1 of [7] are erroneous. One of the authors of [7] (who is also a co-author of this paper) confirmed that somehow incorrect data was entered into Table 1. We present the correct data in this paper.…”

“…We ask the following question to extend the work in [7]. Does there exist a special class of constacyclic codes over Z 4 + uZ 4 (u 2 = 1) whose Z 4 -images (with possibly a different Gray map) produce Z 4 -cyclic codes with improved parameters ?…”