A sequence of binary words of length n is called a cube dominating path, if the Hamming distance between two consecutive words is always one, and every binary word of length n is within Hamming distance one from at least one of these words. If also the first and last words are Hamming distance one apart, the sequence is called a cube dominating cycle. Bounds on the cardinality of such sequences...

Frequency hopping (FH) sequences play a key role in frequency hopping spread spectrum communication systems. It is important to find FH sequences which have simultaneously good Hamming correlation,large family size and large period. In this paper, a new set of FH sequences with large period is proposed, and the Hamming correlation distribution of the new set is investigated. The construction of...

Cartesian products of complete graphs are known as Hamming graphs. Using embeddings into Cartesian products of quotient graphs we characterize subgraphs, induced subgraphs, and isometric subgraphs of Hamming graphs. For instance, a graph G is an induced subgraph of a Hamming graph if and only if there exists a labeling of E(G) fulfilling the following two conditions: (i) incident edges receive ...

We prove a version of the Ray-Chaudhuri{Wilson and Frankl-Wilson theorems for kwise intersections and also generalize a classical code-theoretic result of Delsarte for k-wise Hamming distances. A set of code-words a1; a2; : : : ; ak of length n have k-wise Hamming-distance `, if there are exactly ` such coordinates, where not all of their coordinates coincide (alternatively, exactly n ` of thei...