On the construction of completely regular linear codes from distance — Regular graphs
We are presenting a way of building linear completely regular codes taking a special kind of distance-regular graphs as a starting point.
The parameters of the linear code (length, dimension, corrector capacity, minimum distance, covering radius, ...) are calculable starting from the graph parameters.
We provide three theorems to build completely regular codes starting from a distance-regular graph. Theorem 1 in the case binary or ternary. Theorem 2 which generalizes the previous one, but it adds one restriction to its terms. Theorem 3 which is for the case when the graph is not only distance-regular but also distance-transitive.
In the case that we use distance-regular graphs of diameter 2, that is to say, strongly regular graphs, we prove (theorem 4) that the above construction is dual of Delsarte's construction (see ).
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