Parent-Identifying Codes

Parent-Identifying Codes

For a set C of words of length 4 over an alphabet of size n, and for a, b ∈ C, let D(a, b) be the set of all descendants of a and b, that is, all words x of length 4 where xi ∈ {ai, bi} for all 1 ≤ i ≤ 4. The code C satisfies the Identifiable Parent Property if for any descendant of two code-words one can identify at least one parent. The study of such codes is motivated by questions about sche...

New Bounds on Parent-Identifying Codes: The Case of Multiple Parents

Let C be a code of length n over an alphabet of q letters. A codeword y is called a descendant of a set of t codewords {x, . . . , x} if yi ∈ {xi , . . . , xi} for all i = 1, . . . , n. A code is said to have the Identifiable Parent Property of order t if for any word of length n that is a descendant of at most t codewords (parents), it is possible to identify at least one of them. Let ft(n, q)...

Optimal linear identifying codes

On strongly identifying codes

Lexicographic identifying codes

An identifying code in a graph is a set of vertices which intersects all the symmetric differences between pairs of neighbourhoods of vertices. Not all graphs have identifying codes; those that do are referred to as twin-free. In this paper, we design an algorithm that finds an identifying code in a twin-free graph on n vertices in O(n) binary operations, and returns a failure if the graph is n...