Codes and designs from triangular graphs and their line graphs

Washiela Fish; Khumbo Kumwenda; Eric Mwambene

Open Mathematics (2011)

  • Volume: 9, Issue: 6, page 1411-1423
  • ISSN: 2391-5455

Abstract

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For any prime p, we consider p-ary linear codes obtained from the span over 𝔽 p p of rows of incidence matrices of triangular graphs, differences of the rows and adjacency matrices of line graphs of triangular graphs. We determine parameters of the codes, minimum words and automorphism groups. We also show that the codes can be used for full permutation decoding.

How to cite

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Washiela Fish, Khumbo Kumwenda, and Eric Mwambene. "Codes and designs from triangular graphs and their line graphs." Open Mathematics 9.6 (2011): 1411-1423. <http://eudml.org/doc/269265>.

@article{WashielaFish2011,
abstract = {For any prime p, we consider p-ary linear codes obtained from the span over $\mathbb \{F\}_p $ p of rows of incidence matrices of triangular graphs, differences of the rows and adjacency matrices of line graphs of triangular graphs. We determine parameters of the codes, minimum words and automorphism groups. We also show that the codes can be used for full permutation decoding.},
author = {Washiela Fish, Khumbo Kumwenda, Eric Mwambene},
journal = {Open Mathematics},
keywords = {Automorphism group; Incidence design; Incidence matrix; Line graph; Linear code; Permutation decoding; Triangular graph},
language = {eng},
number = {6},
pages = {1411-1423},
title = {Codes and designs from triangular graphs and their line graphs},
url = {http://eudml.org/doc/269265},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Washiela Fish
AU - Khumbo Kumwenda
AU - Eric Mwambene
TI - Codes and designs from triangular graphs and their line graphs
JO - Open Mathematics
PY - 2011
VL - 9
IS - 6
SP - 1411
EP - 1423
AB - For any prime p, we consider p-ary linear codes obtained from the span over $\mathbb {F}_p $ p of rows of incidence matrices of triangular graphs, differences of the rows and adjacency matrices of line graphs of triangular graphs. We determine parameters of the codes, minimum words and automorphism groups. We also show that the codes can be used for full permutation decoding.
LA - eng
KW - Automorphism group; Incidence design; Incidence matrix; Line graph; Linear code; Permutation decoding; Triangular graph
UR - http://eudml.org/doc/269265
ER -

References

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  15. [15] Kumwenda K., Mwambene E., Codes from graphs related to categorical products of triangular graphs and K n, In: IEEE Information Theory Workshop, Dublin, 30 August–3 September 2010, DOI: 10.1109/CIG.2010.5592662 
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