부산대학교 도서관

Bounds on the size of a code are an important part of coding theory. One of the fundamental problems in coding theory is to find a code with largest possible distance d. Researchers have found different upper and lower bounds on the size of linear and nonlinear codes e.g., Plotkin, Johnson, Singleton, Elias, Linear Programming, Griesmer, Gilbert and Varshamov bounds. In this dissertation we have studied the Singleton bound, which is an upper bound on the minimum distance of a code, and have defined maximum distance separable (MDS) Z2Z4 additive codes. Two different forms of these bounds are presented in this work where we have characterized all maximum distance separable Z2Z4-additive codes with respect to the Singleton bound (MDSS) and strong conditions are given for maximum distance separable Z2Z4-additive codes with respect to the rank bound (MDSR). Generation of new codes has always been an interesting topic, where one can study the properties of these newly generated codes and establish new results. Self-dual codes are an important class of codes. There are numerous constructions of self-dual codes from combinatorial objects. In this work we have given two methods for generating self-dual codes from 3-class association schemes, namely pure construction and bordered construction. Binary self-dual codes are generated by using these two methods from non-symmetric 3-class association schemes and self-dual codes from rectangular association schemes are generated over Zk. Borges, Dougherty and Fernández-Córdoba in 2011 presented a method to generate new Z2Z4-additive self-dual codes from the existing Z2Z4-additive selfdual codes by extending their length. In this work we have verified whether properties like separability, antipodality and code Type are retained or not, when using this method.