Timeline for Lee codes and $n$-torus
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 30, 2011 at 0:39 | comment | added | user16007 | and d=2 I believe. | |
| Jul 30, 2011 at 0:39 | comment | added | user16007 | @Jyrki Lahtonen The Frobenius ring alphabet technique looks interesting. Let me look at it. Do you know a connection of Lee-metric to codes on torus. They look very similar. But at q=5 and n=2, the number of code words are different. I am not sure why this is?? | |
| Jul 21, 2011 at 9:09 | comment | added | Jyrki Lahtonen | @unknown: Just recalled relatively recent studies extending the linear programming bound to Frobenius ring alphabet (Greferath, Byrne, other people from Dublin). IIRC they don't use the Lee-metric though, but something that they refer to as the homogeneous metric that somehow naturally emerges from the Frobenius ring properties. | |
| Jul 21, 2011 at 9:07 | comment | added | Jyrki Lahtonen | @unknown: You did mention the Hamming bound and Glibert-Varshamov bound in your other question. I'm not sure about the others. In the case of the Hamming metric and binary codes the best substitute to the Hamming bound is the so called linear programming bound. It's been ages, so I would need to check things. IIRC the mechanism of that bound depends on a property called 2-point homogeneity of the ambient metric space, and the Lee-metric doesn't have that property. May be the mechanisms of the Elias bound or the Plotkin bound can be generalized? | |
| Jul 21, 2011 at 1:46 | comment | added | user16007 | @Jyrki Lahtonen I have seen only $q=4$ case or only even cases. I have not seen that much of odd cases. Do you know of any asymptotic results? | |
| Jul 20, 2011 at 19:41 | history | answered | Jyrki Lahtonen | CC BY-SA 3.0 |