Related papers: Constructions of Snake-in-the-Box Codes for Rank M…
Sum-rank-metric codes have wide applications in the multishot network coding and the distributed storage. Linearized Reed-Solomon codes, sum-rank BCH codes and their Welch-Berlekamp type decoding algorithms were proposed and studied. They…
Wang et al. (IEEE Transactions on Information Theory, vol. 62, no. 8, 2016) proposed an explicit construction of an $(n=k+2,k)$ Minimum Storage Regenerating (MSR) code with $2$ parity nodes and subpacketization $2^{k/3}$. The number of…
We introduce a new family of binary linear codes suitable for steganographic matrix embedding. The main characteristic of the codes is the staircase random block structure of the generator matrix. We propose an efficient list decoding…
An (n,d)-permutation code is a subset C of Sym(n) such that the Hamming distance d_H between any two distinct elements of C is at least equal to d. In this paper, we use the characterisation of the isometry group of the metric space…
In the rank modulation scheme for flash memories, permutation codes have been studied. In this paper, we study perfect permutation codes in $S_n$, the set of all permutations on $n$ elements, under the Kendall \tau-Metric. We answer one…
In the last decade there has been a great interest in extending results for codes equipped with the Hamming metric to analogous results for codes endowed with the rank metric. This work follows this thread of research and studies the…
The problem of channel code design for the $M$-ary input AWGN channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the encoder is considered. The code design criterion at high SNR…
We consider the problem of constructing a code capable of correcting a single long tandem duplication error of variable length. As the main contribution of this paper, we present a $q$-ary efficiently encodable code of length $n+1$ and…
Let $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$, where $p$ is a prime, and $k, N$ be any positive integers. We denote $R_k=F_{p^m}[u]/\langle u^k\rangle =F_{p^m}+uF_{p^m}+\ldots+u^{k-1}F_{p^m}$ ($u^k=0$) and…
We give the first two algorithms to enumerate all binary words of $\{0,1\}^\ell$ (like Gray codes) while ensuring that the delay and the auxiliary space is independent from $\ell$, i.e., constant time for each word, and constant memory in…
Developing computationally-efficient codes that approach the Shannon-theoretic limits for communication and compression has long been one of the major goals of information and coding theory. There have been significant advances towards this…
This paper studies noisy index coding problems over single-input single-output broadcast channels. The codewords from a chosen index code of length $N$ are transmitted after $2^N$-PSK modulation over an AWGN channel. In "Index Coded PSK…
Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-gap statement says that for a structured set of words -- such…
Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and…
In this paper, we focus on the demodulation/decoding of the complex modulations/codes that approach the Shannon capacity. Theoretically, the maximum likelihood (ML) algorithm can achieve the optimal error performance whereas it has…
We introduce fast-decodable indexing schemes for edit distance which can be used to speed up edit distance computations to near-linear time if one of the strings is indexed by an indexing string $I$. In particular, for every length $n$ and…
A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as…
We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…
The Smatch metric is a popular method for evaluating graph distances, as is necessary, for instance, to assess the performance of semantic graph parsing systems. However, we observe some issues in the metric that jeopardize meaningful…
We consider rank modulation codes for flash memories that allow for handling arbitrary charge-drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked…