Related papers: Convolutional Codes Derived From Group Character C…
We extend the stabilizer formalism to a class of non-additive quantum codes which are constructed from non-linear classical codes. As an example, we present infinite families of non-additive codes which are derived from Goethals and…
We introduce the factor complex of a neural code, and show how intervals and maximal codewords are captured by the combinatorics of factor complexes. We use these results to obtain algebraic and combinatorial characterizations of…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of…
Predictive coding is a message-passing framework initially developed to model information processing in the brain, and now also topic of research in machine learning due to some interesting properties. One of such properties is the natural…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
In this paper, we present a new method to construct solvable groups with derived length four and four character degrees. We then use this method to present a number of new families of groups with derived length four and four character…
The past decade has seen a flurry of research into pattern avoiding permutations but little of it is concerned with their exhaustive generation. Many applications call for exhaustive generation of permutations subject to various constraints…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes that can be described by a $(2,3)$-regular compact graph. In this paper, we introduce a family of $(d_v,d_c)$-regular GLDPC codes with convolutional code…
We introduce alphabet-permutation (AP) codes, a new family of error-correcting codes defined by iteratively applying random coordinate-wise permutations to a fixed initial word. A special case recovers random additive codes and random…
The genetic code is nearly universal, and the arrangement of the codons in the standard codon table is highly non-random. The three main concepts on origin and evolution of the code are the stereochemical theory; the coevolution theory; and…
Group convolutional neural networks are a useful tool for utilizing symmetries known to be in a signal; however, they require that the signal is defined on the group itself. Existing approaches either work directly with group signals, or…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
A key agreement problem is considered that has a biometric or physical identifier, a terminal for key enrollment, and a terminal for reconstruction. A nested convolutional code design is proposed that performs vector quantization during…
This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension…
The automorphism groups of various linear codes are extensively studied yielding insights into the respective code structure. This knowledge is used in, e.g., theoretical analysis and in improving decoding performance, motivating the…
Let $q$ be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on $\mathbb F_q[x_1,\dots,x_m]$ combined with the ideas in (M. Datta and T. Johnsen, 2022). Compared with…
A combinatorial code $\mathcal{C}$ is a collection of subsets of $[n]$, or equivalently a set of points in $\{0,1\}^n$. A morphism of codes is a map from one combinatorial code to another such that the coordinates of points in the image can…
In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms…