Related papers: On the Linear Programming Bound for Lee-codes
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. Here we collect the present knowledge on lower and upper bounds for binary subspace codes for…
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…
In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
A code over a finite field is called locally recoverable code (LRC) if every coordinate symbol can be determined by a small number (at most r, this parameter is called locality) of other coordinate symbols. For a linear code with length n,…
In this work, we consider efficient maximum-likelihood decoding of linear block codes for small-to-moderate block lengths. The presented approach is a branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel (IEEE…
Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a $k$-dimensional linear code over $\mathbb{F}_q$…
Insertion-deletion codes (insdel codes for short) are used for correcting synchronization errors in communications, and in other many interesting fields such as DNA storage, date analysis, race-track memory error correction and language…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
The increasing development of LLMs in code generation has drawn significant attention among researchers. To enhance LLM-based code generation ability, current efforts are predominantly directed towards collecting high-quality datasets and…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
Discrete barycenters are the optimal solutions to mass transport problems for a set of discrete measures. Such transport problems arise in many applications of operations research and statistics. The best known algorithms for exact…
We consider weighted Reed-Muller codes over point ensemble $S_1 \times...\times S_m$ where $S_i$ needs not be of the same size as $S_j$. For $m = 2$ we determine optimal weights and analyze in detail what is the impact of the ratio…
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…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…