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Many non-abelian groups support only group codes that are conformant to abelian group codes

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1 Author(s)
Massey, P.C. ; 53281 Martin Lane, South Bend, IN, USA

Define a group code C over a group (G,*,1) to be a subgroup of the sequence space GZ that is stationary and is not also a subgroup of a sequence space defined on a proper subgroup of G. In addition, consider group codes to be finitely-controllable and complete. This implies that there exist minimal sets of finite-length encoder sequences that will causally encode the group code like an impulse response system over the group G. A non-abelian group code is a group code over a non-abelian group. Two group codes, C1 over G1 and C2 over G2, are defined to be conformant if there exists a bijective mapping between the group codes, ψ:C1→C2, such that it is the component-wise application of a group bijection ψ:G1 →G2 (and with ψ(1)=l)

Published in:

Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on

Date of Conference:

29 Jun-4 Jul 1997