Institute of Mathematics and Informatics Bulgarian Academy of Sciences

Citation:

Serdica Journal of Computing, Vol. 3, No 1, (2009), 15p-22p

Abstract:

One 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.

Description:

Partially supported by the Technical University of Gabrovo under Grant C-801/2008