Timeline for primitive polynomial in $F_2$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2013 at 12:44 | vote | accept | user27932 | ||
| Jun 28, 2013 at 20:35 | comment | added | Dietrich Burde | Such primitive polynomials yield binary Hamming codes. The number of monomials need not be 3 (but odd) in general, e.g., $x^8+x^4+x^3+x^2+1$ is primitive, too (but $x^8+x+1$ not). | |
| Jun 28, 2013 at 18:52 | answer | added | W. Edwin Clark | timeline score: 8 | |
| Jun 28, 2013 at 17:30 | comment | added | Will Sawin | If it is primitive for $d=p$, it will not be primitive for any $d\cong p$ modulo $2^p-1$, because then the polynomial will again be a multiple of $x^p+x+1$. The $d$ for which it is primitive are determined by a prime-like sieve, but they are not the primes. They are almost certainly less frequent than the primes. | |
| Jun 28, 2013 at 17:27 | comment | added | Will Sawin | Not always! $x^5+x+1 = (x^2+x+1)(x^3+x^2+1)$ | |
| Jun 28, 2013 at 16:26 | history | asked | user27932 | CC BY-SA 3.0 |