Yet another variation on minimal linear codes

Gérard  Cohen; Sihem  Mesnager; Hugues  Randriam

doi:10.3934/amc.2016.10.53

Article Contents

2016, Volume 10, Issue 1: 53-61. Doi: 10.3934/amc.2016.10.53

This issue Previous Article On extendability of additive code isometries Next Article Probability estimates for reachability of linear systems defined over finite fields

Yet another variation on minimal linear codes

1.
Télécom ParisTech, UMR 5141, CNRS, 46 rue Barrault, 75634 Paris Cedex 13
2.
University of Paris XIII and Paris VIII, Télécom ParisTech, LAGA, UMR 7539, CNRS, Sorbonne Paris Cité

Received: December 2014

Revised: May 2015

Published: February 2016

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Abstract

Minimal linear codes are linear codes such that the support of every codeword does not contain the support of another linearly independent codeword. Such codes have applications in cryptography, e.g. to secret sharing. We pursue here their study and construct improved asymptotically good families of minimal linear codes. We also consider quasi-minimal, $t$-minimal, and $t$-quasi-minimal linear codes, which are new variations on this notion.

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Mathematics Subject Classification: 94B25, 94B27, 05D40.

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