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Let R be the finite non-chain ring F q 2 + v F q 2 , where v 2 = v and q is an odd prime power. In this paper, we study quantum codes over F q from constacyclic codes over R . We define a class of Gray maps, which preserves the Hermitian dual-containing property of linear codes from R to F q 2 . We study α (1 - 2 v) -constacyclic codes over R , and show that the images of α (1 - 2 v) -constacyclic codes over R under the special Gray map are α 2 -constacyclic codes over F q 2 . Some new non-binary quantum codes are obtained via the Gray map and the Hermitian construction from Hermitian dual-containing α (1 - 2 v) -constacyclic codes over R . [ABSTRACT FROM AUTHOR]

In this paper, we give the structures of all ( 1 + u + v ) -constacyclic codes of length 2 s over F 2 + u F 2 + v F 2 + u v F 2 , we also obtain the number of codewords, and the dual of each constacyclic code. Among other results, we study the form of such constacyclic codes that are self-dual and give the number of these codes. We end by giving all self-dual constacyclic codes of length 2, 4 and 8. [ABSTRACT FROM AUTHOR]

Let $$R=\mathbb {F}_{2^{m}}+u\mathbb {F}_{2^{m}}+\cdots +u^{k}\mathbb {F}_{2^{m}}$$ , where $$\mathbb {F}_{2^{m}}$$ is the finite field with $$2^{m}$$ elements, m is a positive integer, and u is an indeterminate with $$u^{k+1}=0.$$ In this paper, we propose the constructions of two new families of quantum codes obtained from dual-containing cyclic codes of odd length over R. A new Gray map over R is defined, and a sufficient and necessary condition for the existence of dual-containing cyclic codes over R is given. A new family of $$2^{m}$$ -ary quantum codes is obtained via the Gray map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over R. In particular, a new family of binary quantum codes is obtained via the Gray map, the trace map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over R. [ABSTRACT FROM AUTHOR]

In this paper, we study cyclic self-orthogonal codes over Z 2 m for any odd length. We give the generator polynomials of cyclic self-orthogonal codes over Z 2 m . By using these generator polynomials, we obtain a sufficient and necessary condition for the existence of nontrivial cyclic self-orthogonal codes over Z 2 m and determine the number of such codes for a given odd length. Some results about cyclic self-dual codes over Z 2 m are included. [ABSTRACT FROM AUTHOR]

Let R be a finite commutative chain ring and γ be a fixed generator of the maximal ideal of R. For any unit w in R , (1 + w γ) -constacyclic codes over R as a generalization of negacyclic codes over Z 4 are a class of important linear codes. In this paper, based on algebraic structure, the generator polynomials of all torsion codes of (1 + w γ) -constacyclic codes of any length over R are first given. Then, by using these torsion codes, we completely determine the depth spectrums of (1 + w γ) -constacyclic codes over R of any length. [ABSTRACT FROM AUTHOR]