Timeline for Is primality essential in Varshamov's bound?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 14, 2017 at 12:30 | vote | accept | Fedor Petrov | ||
| Jun 14, 2017 at 11:44 | answer | added | Peter Mueller | timeline score: 9 | |
| Jun 12, 2017 at 13:06 | comment | added | Dima Pasechnik | @FedorPetrov - oops, right. I was thinking about upper bounds too much... | |
| Jun 12, 2017 at 10:39 | comment | added | Shahrooz | Gilbert bound is true if the code is not linear, but Varshamov bound is true for linear codes. also, binary cyclic codes are better than the Gilbert- Varshamov bound for lengths up to 1023. For the case $q=6$, we must analyse $Z_6$ codes at the first step. | |
| Jun 12, 2017 at 10:37 | comment | added | Fedor Petrov | @DimaPasechnik It is lower bound: it claims that somehow large code exists. Moreover, even a linear code of such size exists. Of course, not linear code also exists. Your question would be reasonable for upper bounds on the size of a code. | |
| Jun 12, 2017 at 10:28 | comment | added | Dima Pasechnik | @FedorPetrov Varshamov bound is a bound on the code size in terms of $d$, $n$ and $q$, which holds for linear codes. Does it hold for non-linear codes? | |
| Jun 12, 2017 at 9:05 | comment | added | Fedor Petrov | @Dima what do you mean? The claim "linear code exists" implies a claim "code exists". | |
| Jun 12, 2017 at 8:39 | comment | added | Dima Pasechnik | In my answer below I remark that perhaps a more natural question is whether Varshamov's bound holds for non-linear codes. | |
| Jun 12, 2017 at 8:36 | answer | added | Dima Pasechnik | timeline score: 2 | |
| Jun 12, 2017 at 6:36 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
added 1 character in body
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| Jun 12, 2017 at 1:35 | answer | added | kodlu | timeline score: 2 | |
| Jun 11, 2017 at 20:28 | comment | added | Fedor Petrov | @WillSawin Any set of cardinality $q$. We need no other structure for defining Hamming metric on $\Sigma^n$. | |
| Jun 11, 2017 at 19:09 | comment | added | Will Sawin | What is $\Sigma$? A cyclic group? Another abelian group? | |
| Jun 11, 2017 at 13:23 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
edited title
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| Jun 11, 2017 at 12:32 | history | asked | Fedor Petrov | CC BY-SA 3.0 |