In the context of error control in random linear network coding, it is useful to construct codes that comprise well-separated collections of subspaces of a vector space over a finite field.
This thesis concerns the construction of non-constant-dimension projective space codes for adversarial error-correction in random linear network coding. The metric used
is the so-called injection distance introduced by Silva and Kschischang, which perfectly reflects the adversarial nature of the channel.
A Gilbert-Varshamov-type bound for such codes is derived and its asymptotic behaviour is analysed. It is shown that in the limit as the ambient space dimension approaches infinity, the Gilbert-Varshamov bound on the size of non-constant-dimension codes behaves similar to the Gilbert-Varshamov bound on the size of constant-dimension codes contained within the largest Grassmannians in the projective space.
Using the code-construction framework of Etzion and Silberstein, new non-constant-dimension codes are constructed; these codes contain more codewords than comparable codes designed for the subspace metric. To our knowledge this work is the first to address
the construction of non-constant-dimension codes designed for the injection metric.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/18790 |
| Date | 12 February 2010 |
| Creators | Khaleghi, Azadeh |
| Contributors | Kschischang, Frank R. |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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