A numerical semigroup is a co-finite submonoid of the non-negative integers under addition

In the framework of the Theory of Error-Correcting Codes, Feng and Rao introduced a notion of distance for the Weirstrass semigroup at a rational point of an algebraic curve, with decoding purposes. It is a purely combinatorial concept that can be defined for any numerical semigroup. Later on, that notion has been generalised and is used not only in the theory of error correcting codes, but also in cryptography.

Let s be an element of a numerical semigroup S. An element a of S is said to divide s if there exists b in S such that s=a+b. The set of divisors of s is denoted by D(s).
The (classical) Feng-Rao distance is a function d from S into the non negative integers defined by d(m) = min{#(D(n)): n>=m, n in S}.
Replacing the element n in the preceding definition by a set of r elements of S greater than m, one obtains the definition of the r^th Feng-Rao distance.
For a sufficiently large m, there exists a constant, the so-called r^th Feng-Rao number, depending only on r and S, such that the r^th Feng-Rao distance is the classical Feng-Rao distance plus that constant.

An algorithm to compute generalised Feng-Rao numbers will be presented. It can be used in practice and therefore can be extremely useful in the search for formulas for the generalised Feng-Rao numbers of numerical semigroups of certain classes.

The numerical semigroups generated by intervals and those generated by two elements will be considered.

(Joint work with J.I. Farrán, P.A. García-Sánchez and D. Llena.)