6,637 research outputs found
Self-orthogonal codes over a non-unital ring and combinatorial matrices
There is a local ring of order without identity for the
multiplication, defined by generators and relations as
We study a special construction of self-orthogonal codes over based on
combinatorial matrices related to two-class association schemes, Strongly
Regular Graphs (SRG), and Doubly Regular Tournaments (DRT).
We construct quasi self-dual codes over and Type IV codes, that is,
quasi self-dual codes whose all codewords have even Hamming weight. All these
codes can be represented as formally self-dual additive codes over \F_4. The
classical invariant theory bound for the weight enumerators of this class of
codesimproves the known bound on the minimum distance of Type IV codes over
Comment: 18 page
Classification and Galois conjugacy of Hamming maps
We show that for each d>0 the d-dimensional Hamming graph H(d,q) has an
orientably regular surface embedding if and only if q is a prime power p^e. If
q>2 there are up to isomorphism \phi(q-1)/e such maps, all constructed as
Cayley maps for a d-dimensional vector space over the field of order q. We show
that for each such pair d, q the corresponding Belyi pairs are conjugate under
the action of the absolute Galois group, and we determine their minimal field
of definition. We also classify the orientably regular embedding of merged
Hamming graphs for q>3
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
Reconstruction of permutations distorted by single transposition errors
The reconstruction problem for permutations on elements from their
erroneous patterns which are distorted by transpositions is presented in this
paper. It is shown that for any an unknown permutation is uniquely
reconstructible from 4 distinct permutations at transposition distance at most
one from the unknown permutation. The {\it transposition distance} between two
permutations is defined as the least number of transpositions needed to
transform one into the other. The proposed approach is based on the
investigation of structural properties of a corresponding Cayley graph. In the
case of at most two transposition errors it is shown that
erroneous patterns are required in order to reconstruct an unknown permutation.
Similar results are obtained for two particular cases when permutations are
distorted by given transpositions. These results confirm some bounds for
regular graphs which are also presented in this paper.Comment: 5 pages, Report of paper presented at ISIT-200
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