Related papers: Constant Composition Codes as Subcodes of Linear C…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over $\mathbb{F}_q$ having large minimum weights for $q \in \{2,3\}$. Using the characterization, we…
Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of $t$-weight linear codes over ${\mathbb F}_{q}$ are presented with…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
Linear codes generated by component functions of perfect nonlinear (PN) and almost perfect nonlinear (APN) functions and the first-order Reed-Muller codes have been an object of intensive study in coding theory. The objective of this paper…
This paper investigates the concept of self-dual convolutional code. We derive the basic properties of this interesting class of codes and we show how some of the techniques to construct self-dual linear block codes generalize to self-dual…
We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly…
We consider an ensemble of constant composition codes that are subsets of linear codes: while the encoder uses only the constant-composition subcode, the decoder operates as if the full linear code was used, with the motivation of…
In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum…
Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a…
Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties of error-correcting codes. Motivated by recent works…
Constant dimension codes are used for error control in random linear network coding, so that constructions for these codes with large cardinality have achieved wide attention in the last decade. Here, we improve the so-called linkage…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many…
We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords…
Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their simple syndrome readout circuits and potential applications in fault-tolerant quantum computing. However, all families of quantum…
Based on the generic construction of linear codes, we construct linear codes over the ring $\Bbb Z_4$ via posets of the disjoint union of two chains. We determine the Lee weight distributions of the quaternary codes. Moreover, we obtain…
Self-orthogonal codes are of interest as they have important applications in quantum codes, lattices and many areas. In this paper, based on the weakly regular plateaued functions or plateaued Boolean functions, we construct a family of…
Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of two-weight and three-weight linear codes are presented and their…