Related papers: A decoding algorithm for binary linear codes using…
For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…
Standard noncommutative Gr\"obner basis procedures are used for computing ideals of free noncommutative polynomial rings over fields. This paper describes Gr\"obner basis procedures for one-sided ideals in finitely presented noncommutative…
The equivalence of a systematic convolutional encoder as linear state-space control system is first realized and presented through an example. Then, utilizing this structure, a new optimal state-sequence estimator is derived, in the spirit…
In this work, we modify the decoding algorithm for subspace codes by Koetter and Kschischang to get a decoding algorithm for (generalized) twisted Gabidulin codes. The decoding algorithm we present applies to cases where the code is linear…
This paper shows how to decode errors and erasures with Gabidulin codes in sub-quadratic time in the code length, improving previous algorithms which had at least quadratic complexity. The complexity reduction is achieved by accelerating…
The decomposition theory of matroids initiated by Paul Seymour in the 1980's has had an enormous impact on research in matroid theory. This theory, when applied to matrices over the binary field, yields a powerful decomposition theory for…
Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
We study a binary distributed hypothesis testing problem where two agents observe correlated binary vectors and communicate compressed information at the same rate to a central decision maker. In particular, we study linear compression…
We consider binary systematic network codes and investigate their capability of decoding a source message either in full or in part. We carry out a probability analysis, derive closed-form expressions for the decoding probability and show…
A new efficient algorithm is proposed for factoring polynomials over an algebraic extension field. The extension field is defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its Groebner basis, no extra…
In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…
This paper investigates the application of the theoretical algebraic notion of a separable ring extension, in the realm of cyclic convolutional codes or, more generally, ideal codes. We work under very mild conditions, that cover all…
In this paper, we explore a connection between binary hierarchical models, their marginal polytopes and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
In the first part of this article, we consider a Groebner basis of the differential ideal {x_1^2} with respect to "the" weighted lexicographical monomial order and show that its computation is related with an identity involving the…
We compute the nonlinearity of Boolean functions with Groebner basis techniques, providing two algorithms: one over the binary field and the other over the rationals. We also estimate their complexity. Then we show how to improve our…
The binary Hamming codes with parameters $[2^m-1, 2^m-1-m, 3]$ are perfect. Their extended codes have parameters $[2^m, 2^m-1-m, 4]$ and are distance-optimal. The first objective of this paper is to construct a class of binary linear codes…
We present algorithms for classification of linear codes over finite fields, based on canonical augmentation and on lattice point enumeration. We apply these algorithms to obtain classification results over fields with 2, 3 and 4 elements.…
Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…