Orbit codes from forms on vector spaces over a finite field

Angela Aguglia; Antonio Cossidente; Giuseppe Marino; Francesco Pavese; Alessandro Siciliano

doi:10.3934/amc.2020105

Article Contents

2022, Volume 16, Issue 1: 135-155. Doi: 10.3934/amc.2020105

This issue Previous Article A geometric characterization of minimal codes and their asymptotic performance Next Article Infinite families of 2-designs from two classes of binary cyclic codes with three nonzeros

Orbit codes from forms on vector spaces over a finite field

1.
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Bari, I-70126, Italy
2.
Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Potenza, I-85100, Italy
3.
Dipartimento di Matematica e Applicazioni "Renato Caccioppoli", Università degli Studi di Napoli "Federico II", Napoli, I-80138, Italy

^* Corresponding author: Francesco Pavese
^* Corresponding author: Francesco Pavese

Received: April 2020

Revised: July 2020

Early access: August 2020

Published: February 2022

The research was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM).

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Abstract

In this paper we construct different families of orbit codes in the vector spaces of the symmetric bilinear forms, quadratic forms and Hermitian forms on an $ n $-dimensional vector space over the finite field $ {\mathbb F_{q}} $. All these codes admit the general linear group $ {{{{\rm{GL}}}}}(n,q) $ as a transitive automorphism group.

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Mathematics Subject Classification: Primary: 05B25; Secondary: 15A63, 94B25.

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