Ian McLoughlin (NUI Galway)

will speak on

Non-cyclic group ring codes

Time: 4:00PM
Date: Mon 20th October 2008
Location: Mathematical Sciences Seminar Room [map]

Abstract: Cyclic codes are ideals in cyclic group rings (though the term 'group
ring' is not usually used in the description of this relationship).
The ability to use such a framework in analysing these codes has led
to a good understanding of their nature. Recently we have shown that
certain non-cyclic codes (that are not ideals in any group ring over a
cyclic group) are actually ideals in group rings over a dihedral
group. These codes include the extended Hamming (8,4,4) code, the
extended binary Golay code and the unique type II (48,24,12) linear
block code. In this talk I will discuss the construction of group ring
codes in general, and then the construction of those three codes
specifically. It is interesting that these codes can be constructed as
ideals in this way, because they are closely related to a putative
extremal type II (72,36,16) linear block code.

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

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