AbstractThe problem of the existence of perfect and nearly perfect codes over finite alphabets is generalised in two directions. This thesis is concerned with the existence and combinatorial properties of completely regular codes in distance-regular graphs. One of the main tools is the generalisation of Lloyd's Theorem.
There are connections with designs, orthogonal latin squares and finite projective planes and various existence and non-existence results are derived for completely regular codes in three infinite families of distance-regular graphs.
|Date of Award||Oct 1975|