We consider the problem of existence perfect 2-colorings (equitable 2-partitions) Hamming graphs with given parameters. start conditions on parameters and colorings that are necessary for their existence. Next we observe known constructions propose some new ones giving At last, deduce which covered by these give tables admissible in H ( n , q ) small q. Using connection colorings, construct an ...

A code is a subset of the vertex set Hamming graph. The s-neighbours all vertices at distance s from their nearest codeword. C s-elusive if there exists distinct $$C'$$ that equivalent to under full automorphism group graph such and have same s-neighbours. We show minimum an most $$2s+2$$ , with least $$2s+1$$ gives rise q-ary t-design certain parameters. This leads construction of: infinite...

We consider the communication complexity of Hamming distance two strings. Bille et al. [SPIRE 2018] considered longest common prefix (LCP) problem in setting where parties have their strings a compressed form, i.e., represented by Lempel-Ziv 77 factorization (LZ77) with/without self-references. present randomized public-coin protocol for joint computation LZ77 without Although our scheme is hea...