[HTML][HTML] Antiblocking systems and PD-sets

HJ Kroll, R Vincenti - Discrete mathematics, 2008 - Elsevier
… In [6] there are presented examples of PD-sets S for the codes related to … of an antiblocking
system (cf. Section 2). The properties of such an antiblocking system may help to find PD-sets

ANTIBLOCKING SYSTEMS AND PD-SETS

R Vincenti, HJ Kroll - DISCRETE MATHEMATICS, 2008 - research.unipg.it
PD-sets. The question arises whether the Gordon bound is sharp. To handle this problem we
introduce the notion of antiblocking system … the notion of antiblocking system and we show …

[HTML][HTML] How to find small AI-systems for antiblocking decoding

HJ Kroll, R Vincenti - Discrete mathematics, 2012 - Elsevier
… In 2002, we started to look for PD-sets for codes defined by some classical varieties in
finite projective spaces. The information sets of such codes correspond to the basis of the …

[HTML][HTML] Antiblocking decoding

HJ Kroll, R Vincenti - Discrete applied mathematics, 2010 - Elsevier
… An AI-system is a t -antiblocking system consisting of information sets A i . In this way we get
… -systems which are not derived from PD-sets and which are smaller than the known PD-sets. …

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

HJ Kroll, SG Taherian… - Advances in Mathematics …, 2022 - search.ebscohost.com
… Therefore it is of special interest to find small PD-sets and small AI-systems. In 2004 JD
Key, J. Moori, and BG Rodrigues [1] presented PD-sets for the binary codes Cn from triangular …

[PDF][PDF] Partial permutation decoding for simplex codes.

W Fish, JD Key, EC Mwambene - Adv. Math. Commun., 2012 - cecas.clemson.edu
… In this paper we establish the existence of nested s-PD-sets … information systems introduced
by Kroll and Vincenti [11] is … codes, PD-sets and antiblocking information systems are given …

[HTML][HTML] Linear Codes from Projective Varieties: A Survey

R Vincenti - Coding Theory Essentials, 2023 - intechopen.com
… An AI-system (Antiblocking system) is a new decoding algorithm developed by Kroll and …
-system of the same size. But there also may exist AI-systems that are not derived from PD-sets

On the existence of PD-sets: Algorithms arising from automorphism groups of codes.

N Pace, A Sonnino - Advances in Mathematics of …, 2021 - search.ebscohost.com
… (2) If Aut(C) contains PDsets, then find a PD-set of smallest possible size. These problems
… This approach produced several examples of small PDsets that, in some cases, can be …

[PDF][PDF] Third Symposium on Geometry

AC Cöken - J. Geom, 2006 - avesis.atauni.edu.tr
… an antiblocking system. The properties of such an antiblocking system may help to find PD-sets
… Indeed, based on our results concerning antiblocking systems we will present examples …

Minimal PD-sets for codes associated with the graphs , m even

JD Key, BG Rodrigues - Applicable Algebra in Engineering …, 2023 - Springer
… Thus if nested s -PD-sets are found for all \(1<s \le t\) then we can order S as follows: find
an s-PD-set \(S_s\) for each \(0 \le s \le t\) such that \( S_0 \subset S_1 \ldots \subset S_t\) and …