DocumentCode
11580
Title
Group Coding With Complex Isometries
Author
Hye Jung Kim ; Nation, James B. ; Shepler, Anne V.
Author_Institution
Math. & Sci., Kapiolani Community Coll., Honolulu, HI, USA
Volume
61
Issue
1
fYear
2015
fDate
Jan. 2015
Firstpage
33
Lastpage
50
Abstract
We investigate group coding for arbitrary finite groups acting linearly on vector spaces. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using geometric notions of minimal length coset representatives. The infinite family of complex reflection groups G(r, 1, n) produces effective codes of arbitrarily large size that can be decoded in relatively few steps.
Keywords
decoding; geometric codes; group codes; matrix algebra; arbitrary finite group; complex isometry; complex matrix group; correct subgroup decoding; group coding; minimal length coset geometric notion; robust code; vector space; Decoding; Encoding; Noise; Orbits; Robustness; Space vehicles; Vectors; Group codes; group codes; reflection groups; subgroup decoding;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.2014.2365020
Filename
6936375
Link To Document