Related papers: Fast Encoding and Decoding of Gabidulin Codes
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code…
Traditionally, multi-trial error/erasure decoding of Reed-Solomon (RS) codes is based on Bounded Minimum Distance (BMD) decoders with an erasure option. Such decoders have error/erasure tradeoff factor L=2, which means that an error is…
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…
Over fields of characteristic unequal to $2$, we can identify symmetric matrices with homogeneous polynomials of degree $2$. This allows us to view symmetric rank-metric codes as living inside the space of such polynomials. In this paper,…
Algebraic codes that achieve list decoding capacity were recently constructed by a careful ``folding'' of the Reed-Solomon code. The ``low-degree'' nature of this folding operation was crucial to the list decoding algorithm. We show how…
Maximum rank distance codes denoted MRD-codes are the equivalent in rank metric of MDS-codes. Given any integer $q$ power of a prime and any integer $n$ there is a family of MRD-codes of length $n$ over $\FF{q^n}$ having polynomial-time…
A new Chase-type soft-decision decoding algorithm for Reed-Solomon codes is proposed, referred to as tree-based Chase-type algorithm}. The proposed tree-based Chase-type algorithm takes the set of all vectors as the set of testing patterns,…
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that,…
The issue of repairing Reed-Solomon codes currently employed in industry has been sporadically discussed in the literature. In this work we carry out a systematic study of these codes and investigate important aspects of repairing them…
The golden code is a full-rate full-diversity space-time code for two transmit antennas that has a maximal coding gain. Because each codeword conveys four information symbols from an M-ary quadrature-amplitude modulation alphabet, the…
A novel permutation decoding method for Reed-Muller codes is presented. The complexity and the error correction performance of the suggested permutation decoding approach are similar to that of the recursive lists decoder. It is…
In this work we present a new criterion to check if a given rank-metric code is a maximum rank distance (MRD) code. Moreover, we derive a criterion to check if a given MRD code is a generalized Gabidulin code. We then use these results to…
Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit…
In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed-Solomon codes and algebraic geometry codes. This lemma states that two vector…
This paper focuses on Hagiwara codes, which are quantum deletion-correcting codes constructed by the quantum Reed-Solomon codes. Although Hagiwara codes can correct composite errors consisting of deletions and insertions, an efficient…
In this article we construct a new family of linear maximum rank distance (MRD) codes for all parameters. This family contains the only known family for general parameters, the Gabidulin codes, and contains codes inequivalent to the…
We analyze the Guruswami--Sudan list decoding algorithm for Reed--Solomon codes over the complex field for sparse recovery in Compressed Sensing. We propose methods of stabilizing both the interpolation and the root-finding steps against…
We present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by an edge…
This paper presents a new explicit construction for locally repairable codes (LRCs) for distributed storage systems which possess all-symbols locality and maximal possible minimum distance, or equivalently, can tolerate the maximal number…
Reed-Solomon (RS) codes are constructed over a finite field that have been widely employed in storage and communication systems. Many fast encoding/decoding algorithms such as fast Fourier transform (FFT) and modular approach are designed…