Related papers: Almost Cover-Free Codes and Designs
We introduce a definition for \emph{Families of Optimal Binary Non-MDS Erasure Codes} for $[n, k]$ codes over $GF(2)$, and propose an algorithm for finding those families by using hill climbing techniques over Balanced XOR codes. Due to the…
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…
Perfect codes are arguably the most fascinating structures in combinatorial coding theory, and their classification and weight distribution are of considerable interest. This classification also involves the analysis of some related…
Finite covers are a technique for building new structures from simpler ones. The original motivation to study finite covers is in the Ladder theorem of Zilber which describes how totally categorical structures are built from strictly…
Binary code similarity detection is a core task in reverse engineering. It supports malware analysis and vulnerability discovery by identifying semantically similar code in different contexts. Modern methods have progressed from manually…
The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem the optimum mean codeword length of variable-length codes has already been determined. On the…
We analyze the asymptotic performance of nonbinary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group, when the transmission takes place over the binary erasure channel. We propose an efficient…
We construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…
This paper presents a method to calculate the exact average block error probability of some random code ensembles under maximum-likelihood decoding. The proposed method is applicable to various channels and ensembles. The focus is on both…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
A subset $A$ of a finite abelian group is called $(k,\ell)$-sum-free if $kA \cap \ell A=\emptyset.$ In this paper, we extend this concept to compact abelian groups and study the question of how large a measurable $(k,\ell)$-sum-free set can…
Given subsets of uncertain values, we study the problem of identifying the subset of minimum total value (sum of the uncertain values) by querying as few values as possible. This set selection problem falls into the field of explorable…
We analyze a new group testing scheme, termed semi-quantitative group testing, which may be viewed as a concatenation of an adder channel and a discrete quantizer. Our focus is on non-uniform quantizers with arbitrary thresholds. For the…
We study trace codes with defining set $L,$ a subgroup of the multiplicative group of an extension of degree $m$ of the alphabet ring $\mathbb{F}_3+u\mathbb{F}_3+u^{2}\mathbb{F}_{3},$ with $u^{3}=1.$ These codes are abelian, and their…
A general framework is proposed that includes polar codes over arbitrary channels with arbitrary kernels. The asymptotic tradeoff among block length $N$, code rate $R$, and error probability $P$ is analyzed. Given a tradeoff between $N,P$…
Performance of reliable communication over a coherent slow fading channel at high SNR is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains. We study the problem of designing codes that optimally tradeoff…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
Given a group $G$ and a subset $X \subset G$, an element $g \in G$ is called quasi-positive if it is equal to a product of conjugates of elements in the semigroup generated by $X$. This notion is important in the context of braid groups,…
Mixed codes, which are error-correcting codes in the Cartesian product of different-sized spaces, model degrading storage systems well. While such codes have previously been studied for their algebraic properties (e.g., existence of perfect…
The Lloyd Theorem of (Sol\'e, 1989) is combined with the Schwartz-Zippel Lemma of theoretical computer science to derive non-existence results for perfect codes in the Lee metric, NRT metric, mixed Hamming metric, and for the sum-rank…