# On some Optimal (n,t,1,2) and (n,t,1,3) Super Imposed Codes

Serdica Journal of Computing (2009)

- Volume: 3, Issue: 1, page 15-22
- ISSN: 1312-6555

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topManev, Mladen. "On some Optimal (n,t,1,2) and (n,t,1,3) Super Imposed Codes." Serdica Journal of Computing 3.1 (2009): 15-22. <http://eudml.org/doc/11440>.

@article{Manev2009,

abstract = {Partially supported by the Technical University of Gabrovo under Grant C-801/2008One of the main problems in the theory of superimposed codes
is to find the minimum length N for which an (N, T,w, r) superimposed
code exists for given values of T , w and r. Let N(T,w, r) be the minimum
length N for which an (N, T,w, r) superimposed code exists. The (N, T,w, r)
superimposed code is called optimal when N = N(T,w, r). The values of
N(T, 1, 2) are known for T ≤ 12 and the values of N(T, 1, 3) are known
for T ≤ 20. In this work the values of N(T, 1, 2) for 13 ≤ T ≤ 20 and
the value of N(21, 1, 3) are obtained. The optimal superimposed codes with
parameters (9, 10, 1, 2), (10, 13, 1, 2), (11, 14, 1, 2), (11, 15, 1, 2), (11, 16, 1, 2)
and (11, 17, 1, 2) are classified up to equivalence. The optimal (N, T, 1, 3)
superimposed codes for T ≤ 20 are classified up to equivalence.},

author = {Manev, Mladen},

journal = {Serdica Journal of Computing},

keywords = {Superimposed Codes; Classification},

language = {eng},

number = {1},

pages = {15-22},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {On some Optimal (n,t,1,2) and (n,t,1,3) Super Imposed Codes},

url = {http://eudml.org/doc/11440},

volume = {3},

year = {2009},

}

TY - JOUR

AU - Manev, Mladen

TI - On some Optimal (n,t,1,2) and (n,t,1,3) Super Imposed Codes

JO - Serdica Journal of Computing

PY - 2009

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 3

IS - 1

SP - 15

EP - 22

AB - Partially supported by the Technical University of Gabrovo under Grant C-801/2008One of the main problems in the theory of superimposed codes
is to find the minimum length N for which an (N, T,w, r) superimposed
code exists for given values of T , w and r. Let N(T,w, r) be the minimum
length N for which an (N, T,w, r) superimposed code exists. The (N, T,w, r)
superimposed code is called optimal when N = N(T,w, r). The values of
N(T, 1, 2) are known for T ≤ 12 and the values of N(T, 1, 3) are known
for T ≤ 20. In this work the values of N(T, 1, 2) for 13 ≤ T ≤ 20 and
the value of N(21, 1, 3) are obtained. The optimal superimposed codes with
parameters (9, 10, 1, 2), (10, 13, 1, 2), (11, 14, 1, 2), (11, 15, 1, 2), (11, 16, 1, 2)
and (11, 17, 1, 2) are classified up to equivalence. The optimal (N, T, 1, 3)
superimposed codes for T ≤ 20 are classified up to equivalence.

LA - eng

KW - Superimposed Codes; Classification

UR - http://eudml.org/doc/11440

ER -

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