Related papers: Decoding a class of maximum Hermitian rank metric …
We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise…
In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that generally consist of duplicate entries. We first introduce a class of binary matrices called…
Permutation codes in the Ulam metric, which can correct multiple deletions, have been investigated extensively recently. In this work, we are interested in the maximum size of permutation codes in the Ulam metric and aim to design…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
This letter investigates a new class of index coding problems. One sender broadcasts packets to multiple users, each desiring a subset, by exploiting prior knowledge of linear combinations of packets. We refer to this class of problems as…
Minimal codes are a class of linear codes which gained interest in the last years, thanks to their connections to secret sharing schemes. In this paper we provide the weight distribution and the parameters of families of minimal codes…
The study of codes for powerlines communication has garnered much interest over the past decade. Various types of codes such as permutation codes, frequency permutation arrays, and constant composition codes have been proposed over the…
In this letter we consider the ensemble of codes formed by the serial concatenation of a Hamming code and two accumulate codes. We show that this ensemble is asymptotically good, in the sense that most codes in the ensemble have minimum…
In this paper, we study maximal sets of skew lines on Hermitian surfaces. We give a new algorithm to compute these sets and give some computational results for Hermitian surfaces of degrees 3,4, and 5. In more generality, this algorithm…
In this paper we present several classes of asymptotically good concatenated quantum codes and derive lower bounds on the minimum distance and rate of the codes. We compare these bounds with the best-known bound of…
Nested code pairs play a crucial role in the construction of ramp secret sharing schemes [Kurihara et al. 2012] and in the CSS construction of quantum codes [Ketkar et al. 2006]. The important parameters are (1) the codimension, (2) the…
Linear constraints for a matrix polytope with no fractional vertex are investigated as intersecting research among permutation codes, rank modulations, and linear programming methods. By focusing the discussion to the block structure of…
The study of linear codes over a finite field of odd cardinality, derived from determinantal varieties obtained from symmetric matrices of bounded rank, was initiated in a recent paper by the authors. There, one found the minimum distance…
This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
We construct $s$-interleaved linearized Reed--Solomon (ILRS) codes and variants and propose efficient decoding schemes that can correct errors beyond the unique decoding radius in the sum-rank metric. The proposed interpolation-based scheme…
Information set decoding (ISD) algorithms are the best known procedures to solve the decoding problem for general linear codes. These algorithms are hence used for codes without a visible structure, or for which efficient decoders…
We study uniquely decodable codes and list decodable codes in the high-noise regime, specifically codes that are uniquely decodable from $\frac{1-\varepsilon}{2}$ fraction of errors and list decodable from $1-\varepsilon$ fraction of…
We address the problem of computing distances between rankings that take into account similarities between candidates. The need for evaluating such distances is governed by applications as diverse as rank aggregation, bioinformatics, social…
In the recent years, the notion of rank metric in the context of coding theory has known many interesting developments in terms of applications such as space time coding, network coding or public key cryptography. These applications raised…