Related papers: Product Constructions for Perfect Lee Codes
There exists a large literature of construction of convolutional codes with maximal or near maximal free distance. Much less is known about constructions of convolutional codes having optimal or near optimal column distances. In this paper,…
We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields…
Some linear codes associated to maximal algebraic curves via Feng-Rao construction are investigated. In several case, these codes have better minimum distance with respect to the previously known linear codes with same length and dimension.
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…
Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are presented. The first…
Reed-Solomon codes, a type of BCH codes, are widely employed in communication systems, storage devices and consumer electronics. This fact demonstrates the importance of BCH codes -- a family of cyclic codes -- in practice. In theory, BCH…
The present paper mainly studies limits and constructions of insertion and deletion (insdel for short) codes. The paper can be divided into two parts. The first part focuses on various bounds, while the second part concentrates on…
For a pair of given binary perfect codes C and D of lengths t and m respectively, the Mollard construction outputs a perfect code M(C,D) of length tm + t + m, having subcodes C1 and D2, that are obtained from codewords of C and D…
The main conjecture on maximum distance separable (MDS) codes states that, execpt for some special cases, the maximum length of a q-ary linear MDS code is q+1. This conjecture does not hold true for near maximum distance separable codes…
Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair cost by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs have…
We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main…
Linear complementary dual codes (LCD) are linear codes satisfying $C\cap C^{\perp}=\{0\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal…
The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of…
A complete classification of the perfect binary one-error-correcting codes of length 15 as well as their extensions of length 16 was recently carried out in [P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary one-error-correcting…
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…
Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices is bounded in different ways. The duals of matrix product…
Partial spread is important in finite geometry and can be used to construct linear codes. From the results in (Designs, Codes and Cryptography 90:1-15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a…
This paper provides new and improved Singleton-like bounds for Lee metric codes over integer residue rings. We derive the bounds using various novel definitions of generalized Lee weights based on different notions of a support of a linear…
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…