108,299 research outputs found
Large Constant Dimension Codes and Lexicodes
Constant dimension codes, with a prescribed minimum distance, have found
recently an application in network coding. All the codewords in such a code are
subspaces of \F_q^n with a given dimension. A computer search for large
constant dimension codes is usually inefficient since the search space domain
is extremely large. Even so, we found that some constant dimension lexicodes
are larger than other known codes. We show how to make the computer search more
efficient. In this context we present a formula for the computation of the
distance between two subspaces, not necessarily of the same dimension.Comment: submitted for ALCOMA1
Weaving Worldsheet Supermultiplets from the Worldlines Within
Using the fact that every worldsheet is ruled by two (light-cone) copies of
worldlines, the recent classification of off-shell supermultiplets of
N-extended worldline supersymmetry is extended to construct standard off-shell
and also unidextrous (on the half-shell) supermultiplets of worldsheet
(p,q)-supersymmetry with no central extension. In the process, a new class of
error-correcting (even-split doubly-even linear block) codes is introduced and
classified for , providing a graphical method for classification of
such codes and supermultiplets. This also classifies quotients by such codes,
of which many are not tensor products of worldline factors. Also,
supermultiplets that admit a complex structure are found to be depictable by
graphs that have a hallmark twisted reflection symmetry.Comment: Extended version, with added discussion of complex and quaternionic
tensor products demonstrating that certain quotient supermultiplets do not
factorize over any ground fiel
Identifying codes in vertex-transitive graphs and strongly regular graphs
We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2ln(vertical bar V vertical bar) + 1 where V is the set of vertices of the graph. We focus on vertex-transitive graphs for which we can compute the exact fractional solution. There are known examples of vertex-transitive graphs that reach both bounds. We exhibit infinite families of vertex-transitive graphs with integer and fractional identifying codes of order vertical bar V vertical bar(alpha) with alpha is an element of{1/4, 1/3, 2/5}These families are generalized quadrangles (strongly regular graphs based on finite geometries). They also provide examples for metric dimension of graphs
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