Using tools from algebraic graph theory, we draw a link be- tween the maximal order of codes and that of anti-codes. Then using results like the celebrated Erd˝ ...

For instance, both the Hamming and Singleton bounds can derived as an application of a property relating the clique number and the independence number of vertex ...

It is shown how several known bounds on Aq(n,d) and A( n,d, w) can be easily obtained in a single framework and derive some new bounds and present some ...

Building on results from algebraic graph theory and the Erds- Ko-Rado like theorems in extremal combinatorics, we show how several known bounds on codes can ...

We consider a code to be a subset of the vertices of a Hamming graph and the set of neighbours are those vertices not in the code, which are distance one from ...

Dive into the research topics of 'Bounds on codes based on graph theory'. Together they form a unique fingerprint. Graph Theory Keyphrases 100%. Extremal ...

Apr 28, 2015 · It is a simple exercise to see that each Ca is a constant-weight code with minimum Hamming distance 4, i.e., an independent set in J(n,w). Since ...

Abstract. The capacity of a graph is defined as the rate of exponential grow of independent sets in the strong powers of the graph. In strong power, an.

Mar 23, 2014 · I would like to find an upper bound: L(n,d,w) <= f(n,d,w). for a constant weight code L(n,d,w), where w is the maximum weight, ...

Jul 29, 2010 · Hoffman's bound states that χ(G)≥1−λ1(G)λn(G) where λ1(G),λn(G) denote the largest and smallest eigenvalues of the adjacency matrix of G.