295,175 research outputs found
A note on binary completely regular codes with large minimum distance
We classify all binary error correcting completely regular codes of length
with minimum distance .Comment: 4 page
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
Families of nested completely regular codes and distance-regular graphs
In this paper infinite families of linear binary nested completely regular
codes are constructed. They have covering radius equal to or ,
and are -th parts, for of binary (respectively,
extended binary) Hamming codes of length (respectively, ), where
. In the usual way, i.e., as coset graphs, infinite families of embedded
distance-regular coset graphs of diameter equal to or are
constructed. In some cases, the constructed codes are also completely
transitive codes and the corresponding coset graphs are distance-transitive
Diagonally Neighbour Transitive Codes and Frequency Permutation Arrays
Constant composition codes have been proposed as suitable coding schemes to
solve the narrow band and impulse noise problems associated with powerline
communication. In particular, a certain class of constant composition codes
called frequency permutation arrays have been suggested as ideal, in some
sense, for these purposes. In this paper we characterise a family of neighbour
transitive codes in Hamming graphs in which frequency permutation arrays play a
central rode. We also classify all the permutation codes generated by groups in
this family
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