Information on Result #1321568
Linear OA(4129, 160, F4, 68) (dual of [160, 31, 69]-code), using construction X with Varšamov bound based on
- linear OA(4128, 158, F4, 68) (dual of [158, 30, 69]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4124, 152, F4, 68) (dual of [152, 28, 69]-code), using
- 1 times truncation [i] based on linear OA(4125, 153, F4, 69) (dual of [153, 28, 70]-code), using
- a “GraQC†code from Grassl’s database [i]
- 1 times truncation [i] based on linear OA(4125, 153, F4, 69) (dual of [153, 28, 70]-code), using
- linear OA(4124, 154, F4, 65) (dual of [154, 30, 66]-code), using Gilbert–Varšamov bound and bm = 4124 > Vbs−1(k−1) = 430 006062 304145 602123 893766 852203 183374 069895 952139 293430 022722 830240 094686 [i]
- linear OA(42, 4, F4, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,4)), using
- Reed–Solomon code RS(2,4) [i]
- linear OA(4124, 152, F4, 68) (dual of [152, 28, 69]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4128, 159, F4, 67) (dual of [159, 31, 68]-code), using Gilbert–Varšamov bound and bm = 4128 > Vbs−1(k−1) = 110531 885652 233214 410124 221089 771233 164486 691609 315930 623429 174626 028311 499764 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4130, 162, F4, 68) (dual of [162, 32, 69]-code) | [i] | Construction X with Varšamov Bound | |