The Discussion on Hulls of Cyclic Codes over the Ring $\Re ={\mathbb{Z}}_4+v{\mathbb{Z}}_4$, $v^2=v$

Abstract

For odd length $n$, the cyclic codes construction over $\Re ={\mathbb{Z}}_4[v]/⟨v^2-v⟩$ is provided. The hulls of cyclic codes over $\Re$ are studied. The average $2$-dimension $E(n)$ of the hulls of cyclic codes over $\Re$ is also conferred. Among these, the various examples of generators of hulls of cyclic codes over $\Re$ are provided, whose ${\mathbb{Z}}_4$-images are good ${\mathbb{Z}}_4$-linear codes with good parameters.

19 pages