Z 4 Z 4 [u]-ADDITIVE CYCLIC AND CONSTACYCLIC CODES

Habibul Islam , Om Prakash (1) , Patrick Solé (2)

1 University of Delhi
2 I2M - Institut de Mathématiques de Marseille

We study mixed alphabet cyclic and constacyclic codes over the two alphabets Z 4 , the ring of integers modulo 4, and its quadratic extension Z 4 [u] = Z 4 + uZ 4 , u 2 = 0. Their generator polynomials and minimal spanning sets are obtained. Further, under new Gray maps, we nd cyclic, quasi-cyclic codes over Z 4 as the Gray images of both λ-constacyclic and skew λ-constacyclic codes over Z 4 [u]. Moreover, it is proved that the Gray images of Z 4 Z 4 [u]-additive constacyclic and skew Z 4 Z 4 [u]-additive constacyclic codes are generalized quasi-cyclic codes over Z 4. Finally, several new quaternary linear codes are obtained from these cyclic and constacyclic codes.

Domaines: Mathématiques [math]; Informatique [cs]; Théorie de l'information [cs.IT]

Habibul Islam, Om Prakash, Patrick Solé. Z 4 Z 4 [u]-ADDITIVE CYCLIC AND CONSTACYCLIC CODES. Advances in Mathematics of Communications, 2020, ⟨10.3934/amc.xx.xx.xx⟩. ⟨hal-02641416⟩