Hulls of cyclic codes over Z4

MacWilliams identities for linear codes over the ring Z4+uZ4 on the Hermitian inner product

“…First we give the definition of the Lee weight enumerator. Definition 3.3 [8] . Let C be a linear code with length n over R .…”

“…For example, Krotov [7] studied 4 Z -linear Hadamard codes and extended perfect codes. Jitman [8] et al considered Hulls of cyclic codes over 4 Z , etc.…”

Hulls of cyclic serial codes over a finite chain ring

“…When = 0, and with the triple-sequence of a cyclic serial code, by comparing the two sides of Equation (10) in Theorem 1, the following result is obtained.…”

“…Furthermore, in [9] the authors gave the average Euclidean hull dimension of negacyclic codes over a finite field. Recently, the concept of the Euclidean hulls has been generalized to cyclic codes of odd length over Z 4 in [10] where the authors provided an algorithm to determine the type of the Euclidean hull of cyclic codes over Z 4 .…”

“…This is the serial case stated in [13], i.e. the cyclic codes over R whose length n is coprime with p are serial modules over R. We will generalize the techniques used in [10] (for Z 4 ) to obtain the parameters and the average p r -dimensions Euclidean hull of cyclic serial codes over finite chain rings.…”