Duadic and Consta Skew Cyclic Codes Over Certain Frobenius Rings

Abstract

RAMEZ Z. AL-SHORBASSI. Duadic and Consta Skew Cyclic Codes Over Certain Frobenius Rings. Doctor of Philosophy of Science dissertation (Pure Mathematics) . University College of Women for Art, Science and Education, Ain Shams University.

This thesis focuses on study (θ − β)-constacyclic codes and quadratic residue codes over the ring R = Fp + uFp + vFp + uvFp + v2Fp + uv2Fp.

In this thesis, we set some definitions and theorems which will be applied throughout the thesis, we study a class of rings called Frobenius rings. Linear codes, cyclic codes, Constacyclic codes, Skew cyclic codes, and Skew constacyclic codes are studied over the rings Fq + uFq + vFq + uvFq and Fq + uFq + vFq + uvFq + v2Fq + uv2Fq . Finally quadratic residue codes are studied over the rings Fp + uFp + vFp + uvFp, Fp + vFp + v2Fp + v3Fp and Fp + uFp + vFp + uvFp + v2Fp + uv2Fp.