Projects per year
Abstract
General error locator polynomials were introduced in 2005 as an alternative decoding for cyclic codes.
We present now a conjecture on their sparsity which would imply polynomial-time decoding for all cyclic codes.
A general result on the explicit form of the general error locator polynomial for all cyclic codes is given, along
with several results for specific code families, providing evidence to our conjecture.
From these, a theoretical justification of the sparsity of general error locator polynomials is obtained
for all binary cyclic codes with t <= 2 and n<105, as well as for t=3 and n<63, except for some cases
where the conjectured sparsity is proved by a computer check.
Moreover, we summarize all related results, previously published, and we show how they provide further evidence
to our conjecture. Finally, we discuss the link between our conjecture and the complexity of bounded-distance decoding of cyclic codes.
Original language | English |
---|---|
Pages (from-to) | 3641-3557 |
Number of pages | 17 |
Journal | IEEE Transactions on Information Theory |
Volume | 63 |
Issue number | 6 |
Early online date | 7 Apr 2017 |
DOIs | |
Publication status | Published - Jun 2017 |
Keywords
- Bounded-distance decoding
- Symmetric function
- Cyclic codes
- Finite fileds
Fingerprint
Dive into the research topics of 'On the Shape of the General Error Locator Polynomial for Cyclic Codes'. Together they form a unique fingerprint.Projects
- 1 Finished