50,255 research outputs found
Conway Groupoids and Completely Transitive Codes
To each supersimple design \De one associates a `Conway groupoid,' which may be thought of as a natural generalisation of Conway's Mathieu groupoid which is constructed from .
We show that \Sp_{2m}(2) and 2^{2m}.\Sp_{2m}(2) naturally occur as Conway groupoids associated to certain designs. It is shown that the incidence matrix associated to one of these designs generates a new family of completely transitive -linear codes with minimum distance 4 and covering radius 3, whereas the incidence matrix of the other design gives an alternative construction of a
previously known family of completely transitive codes.
We also give a new characterization of and prove that, for a fixed there are finitely many Conway groupoids for which the set of morphisms does not contain all elements of the full alternating group
Binary and Ternary Quasi-perfect Codes with Small Dimensions
The aim of this work is a systematic investigation of the possible parameters
of quasi-perfect (QP) binary and ternary linear codes of small dimensions and
preparing a complete classification of all such codes. First we give a list of
infinite families of QP codes which includes all binary, ternary and quaternary
codes known to is. We continue further with a list of sporadic examples of
binary and ternary QP codes. Later we present the results of our investigation
where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions
up to 13 are classified.Comment: 4 page
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