What is meant by Type II codes?

03 March 2013 1 3K Report

On Z_4, it is defined with respect to Euclidean metric, and on other rings like F2+uF2 it is defined with respect to Lee metric. Why is so? Can anyone please explain or suggest some literature?

Patrick Solé

Well historically Type II codes are the so called doubly even self dual binary codes.(There are five types the Vth being trivial. Search for Gleason Pierce Turyn theorem on divisible codes). Then Conway and Sloane define Type II lattices by analogy. So I introduced Type II Z4 codes because construction A yields Type II lattices (see my paper with Bonnecaze Mourrain and Bachoc), In that setting the Euclidean metric is natural. Now over other rings we want to produce binary Type II codes hence the metric used for F2+uF2 or even F4.

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