Related papers: Linear Codes from Some 2-Designs
Quick Response (QR) code is one of the most worldwide used two-dimensional codes.~Traditional QR codes appear as random collections of black-and-white modules that lack visual semantics and aesthetic elements, which inspires the recent…
Using an algebraic approach based on the theory of Coxeter groups, we design, and describe the performance of, a class of line codes for parallel transmission of $b$ bits over $b+1$ wires that admit especially simple encoding and decoding…
One of the most important and challenging problems in coding theory is to determine the optimal values of the parameters of a linear code and to explicitly construct codes with optimal parameters, or as close to the optimal values as…
We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over…
The linear codes with a few weights have been applied widely in combinatorial designs, secret sharing, association schemes, authentication codes and strongly regular graphs. In this paper, we first correct an erroneous result about the…
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual are trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…
Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their connection with evasiveness properties of the associated $q$-system. Using this result, we…
Designing channel codes under low-latency constraints is one of the most demanding requirements in 5G standards. However, a sharp characterization of the performance of traditional codes is available only in the large block-length limit.…
In this paper we consider further applications of $(n,m)$-functions for the construction of 2-designs. For instance, we provide a new application of the extended Assmus-Mattson theorem, by showing that linear codes of APN functions with the…
The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The…
In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including…
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…
When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted…
We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional…
A linear code of length $n$ over a finite chain ring $R$ with residue field $\F_q$ is a $R$-submodule of $R^n$. A $R$-linear code is a code over $\F_q$ (not necessarily linear) which is the generalized Gray map image of a linear code over…
We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear codes has a uniform weight spectrum if the number of vectors…
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions…
A general lossless joint source-channel coding scheme based on linear codes is proposed and then analyzed in this paper. It is shown that a linear code with good joint spectrum can be used to establish limit-approaching joint source-channel…