Related papers: Decoding twisted permutation codes

In this paper we present a new class of convolutional codes that admits an efficient al- gebraic decoding algorithm. We study some of its properties and show that it can decode interesting sequences of errors patterns. The second part of…

We give a quantum algorithm for solving a shifted multiplicative character problem over Z/nZ and finite fields. We show that the algorithm can be interpreted as a matrix factorization or as solving a deconvolution problem and give…

We show how real-number codes can be used to compress correlated sources, and establish a new framework for lossy distributed source coding, in which we quantize compressed sources instead of compressing quantized sources. This change in…

We consider the problem of computing the Fourier transform of high-dimensional vectors, distributedly over a cluster of machines consisting of a master node and multiple worker nodes, where the worker nodes can only store and process a…

The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…

This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…

List decoding of Hermitian codes is reformulated to allow an efficient and simple algorithm for the interpolation step. The algorithm is developed using the theory of Groebner bases of modules. The computational complexity of the algorithm…

A permutoid is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there can exist no algorithm that…

We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…

Lifted Reed-Solomon codes are a natural affine-invariant family of error-correcting codes which generalize Reed-Muller codes. They were known to have efficient local-testing and local-decoding algorithms (comparable to the known algorithms…

In this paper, we propose an analysis of the automorphism group of polar codes, with the scope of designing codes tailored for automorphism ensemble (AE) decoding. We prove the equivalence between the notion of decreasing monomial codes and…

We present an algorithm to construct quantum circuits for encoding and inverse encoding of quantum convolutional codes. We show that any quantum convolutional code contains a subcode of finite index which has a non-catastrophic encoding…

R. Gupta, P. Gahlyan and R.K. Sharma presented three classes of permutation trinomials over $\mathbb{F}_{q^3}$ in Finite Fields and Their Applications. In this paper, we employ the local method to prove that those polynomials are indeed…

Hybrid codes simultaneously encode both quantum and classical information into physical qubits. We give several general results about hybrid codes, most notably that the quantum codes comprising a genuine hybrid code must be impure and that…

The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. From a…

We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite…

We show that quantum expander codes, a constant-rate family of quantum LDPC codes, with the quasi-linear time decoding algorithm of Leverrier, Tillich and Z\'emor can correct a constant fraction of random errors with very high probability.…

In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…

We give a general constructive proof for hierarchical coordinatizations (Lagrange Decompositions) of permutation groups. The generalization originates from the investigation of how the subgroup chains of finite permutation groups yield…

We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.