Partial linear spaces and identifying codes

Partial linear spaces and identifying codes

Let (P ,L, I) be a partial linear space and X ⊆ P ∪ L. Let us denote by (X)I = ⋃ x∈X {y : yIx} and by [X] = (X)I ∪ X. With this terminology a partial linear space (P ,L, I) is said to admit a (1,≤ k)-identifying code if and only if the sets [X] are mutually different for all X ⊆ P ∪ L with |X| ≤ k. In this paper we give a characterization of k-regular partial linear spaces admitting a (1,≤ k)-i...

Regular parcial linear spaces admitting (1;≤ k)-identifying codes

Let (P ,L, I) be a partial linear space and X ⊆ P ∪ L. Let us denote by (X)I = ⋃ x∈X{y : yIx} and by [X ] = (X)I ∪ X . With this terminology a partial linear space (P ,L, I) is said to admit a (1,≤ k)-identifying code if and only if the sets [X ] are mutually different for all X ⊆ P ∪L with |X | ≤ k. In this paper we give a characterization of k-regular partial linear spaces admitting a (1,≤ k)...

Optimal linear identifying codes

Linear codes from projective spaces

The linear code Cs,t(n, q) of s-spaces and t-spaces in a projective space PG(n, q), q = ph, p prime, is defined as the vector space spanned over Fp by the rows of the incidence matrix of s-spaces and t-spaces. This code generalises the code of points and lines in a projective plane, which has been intensively studied since the 1970’s. In this paper, we give an overview of what is currently know...

Identifying and Locating- Dominating Codes in Binary Hamming Spaces Identifying and Locating-Dominating Codes in Binary Hamming Spaces

Acknowledgements First of all I want to thank my supervisor Professor Iiro Honkala for his continuous support, and patience when long breaks in research took place. Many discussions with Iiro, his collaboration, suggestions for research topics, and careful proofreading made this work possible. I also want to thank Dr. Tero Laihonen for many inspiring discussions, suggestions for research topics...