Hulls of Cyclic Codes over Z_4

06/20/2018

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by   Somphong Jitman, et al.

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The hulls of linear and cyclic codes over finite fields have been of interest and extensively studied due to their wide applications. In this paper, the hulls of cyclic codes of length n over the ring Z_4 have been focused on. Their characterization has been established in terms of the generators viewed as ideals in the quotient ring Z_4[x]/〈 x^n-1〉. An algorithm for computing the types of the hulls of cyclic codes of arbitrary odd length over Z_4 has been given. The average 2-dimension E(n) of the hulls of cyclic codes of odd length n over Z_4 has been established. A general formula for E(n) has been provided together with its upper and lower bounds. It turns out that E(n) grows the same rate as n.