Combining subspace codes

Antonio Cossidente; Sascha Kurz; Giuseppe Marino; Francesco Pavese

doi:10.3934/amc.2021007

Article Contents

2023, Volume 17, Issue 3: 536-550. Doi: 10.3934/amc.2021007

This issue Previous Article Several formulas for Bernoulli numbers and polynomials Next Article On the correlation measures of orders $ 3 $ and $ 4 $ of binary sequence of period $ p^2 $ derived from Fermat quotients

Combining subspace codes

1.
Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Contrada Macchia Romana, 85100, Potenza, Italy
2.
Mathematisches Institut, Universität Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany
3.
Dipartimento di Matematica e Applicazioni "Renato Caccioppoli", Università degli Studi di Napoli "Federico II", Complesso Universitario di Monte Sant'Angelo, Cupa Nuova Cintia 21, 80126, Napoli, Italy
4.
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy

Received: November 2020

Revised: February 2021

Early access: April 2021

Published: June 2023

The work of the first, third and fourth author was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA–INdAM)

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Abstract

In the context of constant-dimension subspace codes, an important problem is to determine the largest possible size $ A_q(n, d; k) $ of codes whose codewords are $ k $-subspaces of $ {\mathbb F}_q^n $ with minimum subspace distance $ d $. Here in order to obtain improved constructions, we investigate several approaches to combine subspace codes. This allow us to present improvements on the lower bounds for constant-dimension subspace codes for many parameters, including $ A_q(10, 4; 5) $, $ A_q(12, 4; 4) $, $ A_q(12, 6, 6) $ and $ A_q(16, 4; 4) $.

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Mathematics Subject Classification: Primary: 51E20; Secondary: 05B25, 94B65.

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