Polyadic Cyclic Codes over a Non-Chain Ring  

作　　者：Mokshi Goyal Madhu Raka Mokshi Goyal;Madhu Raka(Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India)

机构地区：[1]Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India

出　　处：《Journal of Computer and Communications》2021年第5期36-57,共22页电脑和通信（英文）

摘　　要：Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F_q. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i>_q</i>. Some examples are also given to illustrate this.Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F_q. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i>_q</i>. Some examples are also given to illustrate this.

关 键 词：Polyadic Codes and Their Extensions Griesmer Bound Gray Map Self-Dual and Self-Orthogonal Codes Isodual Codes LCD Codes 

分 类 号：O15[理学—数学]