Related Experiment Video
Updated: Mar 29, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
Published on: March 18, 2019
Cyclicity of Binary Group Codes
Beatriz García García1, Consuelo Martínez López1, Ignacio F Rúa1
1Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain.
Abstract:
In this paper, we study the cyclicity of binary group codes, identifying them as ideals in a group algebra. We focus on the construction of ω|ω¯ codes, proving that they are self-dual group codes over the abelian group C2×Ck. We demonstrate that for even integers k>2, if the polynomial xk-1 splits into self-reciprocal irreducible factors, these codes are not permutationally equivalent to any cyclic code. Additionally, we present computational results for binary group codes of length n<24 using the MAGMA software (V2.29-4). These results confirm that while all cyclic codes in this range are equivalent to abelian group codes, there exist non-cyclic group codes that cannot be realized as ideals in a cyclic group algebra, highlighting the strictly larger scope of the class of group codes.
Related Concept Videos
Stereoisomerism of Cyclic Compounds
Crystallographic Point Groups
Disubstituted Cyclohexanes: cis-trans Isomerism
In cyclohexane, the substituents can occupy different positions generating distinct isomers....
Cycloalkanes
The IUPAC nomenclature of cycloalkanes follows similar rules that apply to...
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
Second Uniqueness Theorem
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...

