Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths

Baicheva, Tsonka, and Topalova, Svetlana. "Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths." Serdica Journal of Computing 9.1 (2015): 83-92. <http://eudml.org/doc/281509>.

@article{Baicheva2015,
abstract = {Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant weight codes. Therefore the classification of (v, 3, 1) OOCs holds for them too. Some of the classified (v, 3, 1) OOCs are perfect and they are equivalent to cyclic Steiner triple systems of order v and (v, 3, 1) cyclic difference families.},
author = {Baicheva, Tsonka, Topalova, Svetlana},
journal = {Serdica Journal of Computing},
keywords = {Optical Orthogonal Codes; Cyclic Steiner Triple Systems; Binary Cyclically Permutable Constant Weight Codes; Code Division Multiple Access System; optical orthogonal code; classification; binary constant weight code; combinatorial design; cyclic group},
language = {eng},
number = {1},
pages = {83-92},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths},
url = {http://eudml.org/doc/281509},
volume = {9},
year = {2015},
}

TY - JOUR
AU - Baicheva, Tsonka
AU - Topalova, Svetlana
TI - Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths
JO - Serdica Journal of Computing
PY - 2015
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 9
IS - 1
SP - 83
EP - 92
AB - Dedicated to the memory of the late professor Stefan Dodunekov on the occasion of his 70th anniversary. We classify up to multiplier equivalence maximal (v, 3, 1) optical orthogonal codes (OOCs) with v ≤ 61 and maximal (v, 3, 2, 1) OOCs with v ≤ 99. There is a one-to-one correspondence between maximal (v, 3, 1) OOCs, maximal cyclic binary constant weight codes of weight 3 and minimum dis tance 4, (v, 3; ⌊(v − 1)/6⌋) difference packings, and maximal (v, 3, 1) binary cyclically permutable constant weight codes. Therefore the classification of (v, 3, 1) OOCs holds for them too. Some of the classified (v, 3, 1) OOCs are perfect and they are equivalent to cyclic Steiner triple systems of order v and (v, 3, 1) cyclic difference families.
LA - eng
KW - Optical Orthogonal Codes; Cyclic Steiner Triple Systems; Binary Cyclically Permutable Constant Weight Codes; Code Division Multiple Access System; optical orthogonal code; classification; binary constant weight code; combinatorial design; cyclic group
UR - http://eudml.org/doc/281509
ER -