Timeline for When are Hamming codes cyclic?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 8, 2020 at 17:39 | comment | added | azimut | @SteveHuntsman thank you. I just checked that source: It shows that for a primitive element $\alpha$ of $\mathbb{F}_{q^r}$, the cyclic code with check polynomial given by $\alpha^{q-1}$ is a Hamming code if and only if q-1 and r are coprime. But I don't see how this is a full proof of the direction ⇒, because we don't know yet that the cyclic description of a Hamming code is necessarily of the form studied in Th. 5.5.1. For example, the check polynomial might not be irreducible. | |
| Oct 8, 2020 at 12:49 | comment | added | Steve Huntsman | See Theorem 5.5.1 of Algebraic Codes for Data Transmission by Blahut. | |
| Oct 8, 2020 at 9:17 | comment | added | azimut | @GerryMyerson I'm happy when people care for my question. Also interesting that this statement has been touched both on MO and math.SE in the past, but the missing direction has always been dodged. It's the same situation as in the literature that I've checked, for example the book of Huffman and Pless. | |
| Oct 8, 2020 at 9:05 | comment | added | Gerry Myerson | Sorry, I saw the links to m.se and missed the link to MO. | |
| Oct 8, 2020 at 9:01 | comment | added | azimut | @GerryMyerson thank you. In fact, I came across of that answer when searching MO. I've already linked that answer above. But as all sources that I've checked, the "interesting" direction is not there. | |
| Oct 8, 2020 at 8:54 | comment | added | Gerry Myerson | The direction that you can already prove is proved in an answer to this earlier MO question, mathoverflow.net/questions/145345/cyclic-hamming-code | |
| Oct 8, 2020 at 8:15 | history | asked | azimut | CC BY-SA 4.0 |