Dr Habil Marcus Greferath (UCD)

will speak on

Some new insight into the algebraic representation of Best's $(10,40,4)$ code

Time: 4:00PM
Date: Mon 29th March 2010
Location: Mathematical Sciences Seminar Room [map]

Abstract: Best's (10,40,40) code is a binary code with an optimal number of codewords.
By its cardinality it is apparent that it cannot be represented as a linear code over any local
ring alphabet over a local ring. Nonetheless, it was represented as a non-linear (5,40,4)
code over ${mathbb Z}_4$ by Conway and Sloane: the charm of this representation in terms
of this pentacode stems from the fact that it gives rise to more insight into the structure of
the code in question. This talk revisits the pentacode and derives a so far unknown algebraic
representation for it.

(This talk is part of the Algebra and Number Theory series.)

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