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Recently, linear codes with few weights have been widely studied, since they have applications in data storage systems, communication systems and consumer electronics. In this paper, we present a class of three-weight and five-weight linear codes over F p , where p is an odd prime and F p denotes a finite field with p elements. The weight distributions of the linear codes constructed in this paper are also settled. Moreover, the linear codes illustrated in the paper may have applications in secret sharing schemes. [ABSTRACT FROM AUTHOR]

Let p be an odd prime number. In this paper, we construct 2 (2 p − 3) classes of codes over the ring R = F p + u F p , u 2 = 0 , which are associated with down sets. We compute the Lee weight distributions of the 2 (2 p − 3) classes of codes when the down sets are generated by a single maximal element. Moreover, by using the Gray map of the linear codes over R , we find out 2 (p − 1) classes of p -ary distance optimal linear codes. Two of them meet the Griesmer bound. [ABSTRACT FROM AUTHOR]

In this paper, we construct a class of linear codes over the local ring R = F q + u F q and determine the Lee distribution by employing character sums. Using the Gray map, we obtain a class of linear codes with two weights over F q . These linear codes are proved to be optimal with respect to the Griesmer bound. Notably, the parameters of these linear codes are flexible and new. As an application, we employ these linear codes to construct association schemes. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complete weight enumerators of two classes of irreducible cyclic codes. We present the explicit complete weight enumerator of the irreducible cyclic codes. Furthermore, we obtain a class of optimal constant composition codes from irreducible cyclic codes. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the following two hypercube coloring problems: given and , find the minimum number of colors, denoted as (resp. ), needed to color the vertices of the -cube such that any two vertices with Hamming distance at most (resp. exactly ) have different colors. These problems originally arose in the study of the scalability of optical networks. Using methods in coding theory, we show that for any odd number , and give two upper bounds on . The first upper bound improves on that of Kim, Du and Pardalos. The second upper bound improves on the first one for small . Furthermore, we derive an inequality on and . [Copyright &y& Elsevier]

Abstract: In this paper, we determine explicitly the zeta polynomials of near-MDS codes and obtain necessary and sufficient conditions for near-MDS codes to satisfy the Riemann hypothesis analogue. [Copyright &y& Elsevier]