On $\mathbb{Z}_4\mathbb{Z}_4[u^3]$-additive constacyclic codes

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

1 IITP - Indian Institute of Technology Patna
2 I2M - Institut de Mathématiques de Marseille

Let Z 4 be the ring of integers modulo 4. This paper studies mixed alphabets Z 4 Z 4 [u 3 ]-additive cyclic and λ-constacyclic codes for units λ = 1 + 2u 2 , 3 + 2u 2. First, we obtain the generator polynomials and minimal generating set of additive cyclic codes. Then we extend our study to determine the structure of additive constacyclic codes. Further, we dene some Gray maps and obtain Z 4-images of such codes. Finally, we present numerical examples that include six new and two best-known quaternary linear codes.

Mots clés: Additive code; Cyclic code; Constacyclic code; Gray map

Domaines: Théorie de l'information [cs.IT]

Om Prakash, Shikha Yadav, Habibul Islam, Patrick Solé. On $\mathbb{Z}_4\mathbb{Z}_4[u^3]$-additive constacyclic codes. Advances in Mathematics of Communications, 2022, ⟨10.3934/amc.xx.xx.xx⟩. ⟨hal-03581388⟩