Search

In this paper, we construct MacDonald codes of type α over the ring F2 + uF2 + νF2, where u² = u, ν² is the field of two elements and investigate their properties such as torsion codes and weight distributions. [ABSTRACT FROM AUTHOR]

In this paper, we study on modules that have a weak (ample) δ-supplement in every extension which are adapted Zöschinger's modules with the properties (E) and (EE). It is shown that: (1) Direct summands of modules with the property δ-(CWE) have the property δ-(CWE); (2) For a module M, if every submodule of M has the property δ-(CWE) then so does M; (3) For a ring R, R is δ-semilocal iff every R-module has the property δ-(CWE); (4) Every factor module of a finitely generated module that has the property δ-(CWE) also has the property δ-(CWE) under a special condition; (5) Let M be a module and L be a submodule of M such that L <<#948; M. If the factor module M/L has the property δ-(CWE), then so does M; (6) On a semisimple module the concepts of modules that have the property δ-(CE) and δ-(CWE) coincide with each other. [ABSTRACT FROM AUTHOR]

Let R be a ring and M be a left R - module. M is called cofinitely generalized weak supplemented (or briefly CGWS-module) if every cofinite submodule of M has a generalized weak supplement in M. In this paper, we give various properties of that kind of modules. It is shown that (1) A module M is CGWS-module if and only if every maximal submodule has a generalized weak supplement in M. (2) The class of cofinitely generalized weak supplemented modules are closed under taking homomorphic images, arbitrary sums, generalized covers and short exact sequences. (3) A ring R is semilocal if and only if every left R - module is a CGWS-module.(4) A commutative domain R is hsemilocal if and only if every torsion R - module is cofinitely generalized weak supplemented. [ABSTRACT FROM AUTHOR]

Some results are generalized on linear codes over in [15] to the ring , where is an odd prime number. The Gray images of cyclic and quasi-cyclic codes over are obtained. The parameters of quantum error correcting codes are obtained from negacyclic codes over . A nontrivial automorphism on the ring is determined. By using this, the skew cyclic, skew quasi-cyclic, skew constacyclic codes over are introduced. The number of distinct skew cyclic codes over is given. The Gray images of skew codes over are obtained. The quasi-constacyclic and skew quasi-constacyclic codes over are introduced. MacWilliams identities of linear codes over are given. [ABSTRACT FROM AUTHOR]

In this paper, we study skew cyclic and quasi cyclic codes over the ring S = F2 + uF2 + vF2 where u2 = u, v2 = v, uv = vu = 0. We investigate the structural properties of them. Using a Gray map on S we obtain the MacWilliams identities for codes over S. The relationships between Symmetrized, Lee and Hamming weight enumerator are determined. [ABSTRACT FROM AUTHOR]

In this paper, we study the structure of cyclic, quasi-cyclic codes and their skew codes over the finite ring , for . The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic codes over are obtained. A necessary and sufficient condition for cyclic code over that contains its dual has been given. The parameters of quantum error correcting codes are obtained from cyclic codes over . [ABSTRACT FROM AUTHOR]

In this paper, quantum codes from cyclic codes over A2 = F2 + uF2 + vF2 + uvF2, u2 = u, v2 = v, uv = vu, for arbitrary length n have been constructed. It is shown that if C is self orthogonal over A2, then so is Ψ(C), where Ψ is a Gray map. A necessary and sufficient condition for cyclic codes over A2 that contains its dual has also been given. Finally, the parameters of quantum error correcting codes are obtained from cyclic codes over A2. [ABSTRACT FROM AUTHOR]