Published September 1, 2012
| Version Submitted
Journal Article
Open
Codes as Fractals and Noncommutative Spaces
Abstract
We consider the CSS algorithm relating self-orthogonal classical linear codes to q-ary quantum stabilizer codes and we show that to such a pair of a classical and a quantum code one can associate geometric spaces constructed using methods from noncommutative geometry, arising from rational noncommutative tori and finite abelian group actions on Cuntz algebras and fractals associated to the classical codes.
Additional Information
© 2012 Springer Basel AG. Received: 23 August 2011; Revised: 10 April 2012; Accepted: 21 April 2012; Published online 02 June 2012. M. Marcolli is partially supported by NSF grants DMS-0901221 and DMS-1007207. C. Perez was supported for this project by a Caltech Summer Undergraduate Research Fellowship.Attached Files
Submitted - 1107.5782v1.pdf
Files
1107.5782v1.pdf
Additional details
Identifiers
- Eprint ID
- 37668
- Resolver ID
- CaltechAUTHORS:20130328-095244455
Related works
- Describes
- http://arxiv.org/abs/1107.5782 (URL)
Funding
- NSF
- DMS-0901221
- NSF
- DMS-1007207
- Caltech Summer Undergraduate Research Fellowship (SURF)
Dates
- Created
-
2013-04-10Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field
Caltech Custom Metadata
- Caltech groups
- Mathematics Department