Contraction of cyclic codes over finite chain rings

Galois hulls of cyclic serial codes over a finite chain ring

“…In [6], the authors introduced and studied the Galois closure of a linear code C over R of length n as follows,…”

“…where d is a divisor of r. Recall that for any linear code C over R of length n, its subring subcode is given by Res d (C) = C ∩(S d ) n . In [6] it is shown that σ d -invariant, if and only if, T d (C) = Res d (C) if and only if, C = Ext(Res d (C)). For ∈ {0, 1, .…”

“…An important class of linear codes over rings is the class of cyclic codes. They have been studied in a series of papers ( see [4,6,2,7,13,14]). In particular, Dinho and Permouth [4] gave algebraic structure of simple root cyclic codes over finite chain rings R. Martínez and Rúa [13] generalized these results to multivariable cyclic codes over R. Free cyclic serial codes have been determined by using cyclotomic cosets and trace map over finite chain rings R by Fotue and Mouaha in [6].…”

“…They have been studied in a series of papers ( see [4,6,2,7,13,14]). In particular, Dinho and Permouth [4] gave algebraic structure of simple root cyclic codes over finite chain rings R. Martínez and Rúa [13] generalized these results to multivariable cyclic codes over R. Free cyclic serial codes have been determined by using cyclotomic cosets and trace map over finite chain rings R by Fotue and Mouaha in [6]. It is clear that the Euclidean hull of cyclic codes is also cyclic, two special families of cyclic codes are of great interest, namely linear complementary dual codes, which are codes whose Euclidean hull is trivial (see for example [3]) and self-orthogonal codes, which are linear codes whose Euclidean hulls is the whole code (see for example [20].…”

On polycyclic codes over a finite chain ring

“…Cyclicity of codes weight of some polycyclic codes over Galois rings was established. Also in [4] some classes of constacyclic codes over finite chain rings were characterized via cyclotomic cosets as contraction of some cyclic codes. In [11], the authors studied the algebraic structure of a class of linear codes over finite chain rings containing the polycyclic codes.…”