Skew constacyclic codes over a family of rings

In this thesis, skew constacyclic codes are investigated to obtain code families with a high number of elements and minimum distance on a finite, unitary, commutative ring family B_q=F_q+v_1F_q+v_2F_q+v_3F_q+v_4F_q+v_1v_2F_q, where v_i^2=v_i, v_1v_2=v_2v_1, v_iv_j=v_jv_i=0 (i=1,2,3,4, j=3,4, i≠j) and 𝑝 is an odd prime, 𝑚 is a positive integer and 𝑞 = 𝑝^𝑚, using a non-trivial 𝛩-automorphism. Their polynomial representations have been determined. In the first section, a brief overview of the history of coding is provided, along with discussions on its applications. Subsequently, the emergence of coding theory and its fundamental problems are discussed. Finally, literature information related to cyclic, skew cyclic and skew constacyclic codes is presented. In the second section, basic definitions and theorems related to algebra and coding theory are provided. In the third section, the ring family B_q=F_q+v_1F_q+v_2F_q+v_3F_q+v_4F_q+v_1v_2F_q is introduced. A Gray map from 𝐵_𝑞^𝑛 to 𝔽_𝑞^6𝑛 is defined and cyclic codes over 𝔽_𝑞^6 are given. Then, a non-trivial 𝛩-automorphism is defined over 𝐵𝐵𝑞𝑞 and using this automorphism, the 𝐵𝑞[𝑥,𝛩] skew polynomial ring is constructed. Finally, skew 𝜆-constacyclic codes over this ring, along with their properties, are defined and some examples are given.