Optimal antiblocking systems of information sets for the binary codes related to triangular graphs

Hans-Joachim Kroll; Sayed-Ghahreman Taherian; Rita Vincenti

doi:10.3934/amc.2020107

Article Contents

2022, Volume 16, Issue 1: 169-183. Doi: 10.3934/amc.2020107

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Optimal antiblocking systems of information sets for the binary codes related to triangular graphs

1.
Zentrum Mathematik, Technische Universität München, 80290 München, Germany
2.
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran
3.
Dipartimento di Matematica e Informatica Università degli Studi di Perugia, Via Vanvitelli 106123 Perugia, Italy

^* Corresponding author: Hans-Joachim Kroll
^* Corresponding author: Hans-Joachim Kroll

Dedicated to Professor Helmut Karzel on the occasion of his 92^nd birthday.

Received: July 2020

Early access: August 2020

Published: February 2022

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Abstract

We present AI-systems for the binary codes obtained from the adjacency relation of the triangular graphs $ T(n) $ for any $ n\ge 5 $. These AI-systems are optimal and have for $ n $ odd the full error-correcting capability.

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Mathematics Subject Classification: Primary: 94B05, 94B35.

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Figure . The set $\{x, y\}, \; x < y $ belongs to $\mathcal A_l$ iff $l$ is placed in $(x, y)$

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References

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