Hulls of Cyclic Codes over the Ring F2 + vF2

Somphong Jitman, Ekkasit Sangwisut

Abstract

Hulls of linear codes over finite fields have been introduced and become of interest due to their wide practical applications. Recently, the concept of hulls has been generalized to linear and cyclic codes over the finite chain ring Z4. In this paper, hulls of cyclic codes over a non-chain ring F2 + vF2are studied, where v^2 = v. The hull dimensions and the average hull dimension E(n) of cyclic codes of length n over F2 + vF2 are determined. Asymptotically, if n is odd, it turns out that E(n) is zero or it grows the same rate as n.