Information on Result #1300544
Linear OA(4179, 222, F4, 93) (dual of [222, 43, 94]-code), using construction X with Varšamov bound based on
- linear OA(4178, 220, F4, 93) (dual of [220, 42, 94]-code), using
- 2 times truncation [i] based on linear OA(4180, 222, F4, 95) (dual of [222, 42, 96]-code), using
- concatenation of two codes [i] based on
- linear OA(6423, 37, F64, 23) (dual of [37, 14, 24]-code or 37-arc in PG(22,64)), using
- discarding factors / shortening the dual code based on linear OA(6423, 64, F64, 23) (dual of [64, 41, 24]-code or 64-arc in PG(22,64)), using
- Reed–Solomon code RS(41,64) [i]
- discarding factors / shortening the dual code based on linear OA(6423, 64, F64, 23) (dual of [64, 41, 24]-code or 64-arc in PG(22,64)), using
- linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
- linear OA(6423, 37, F64, 23) (dual of [37, 14, 24]-code or 37-arc in PG(22,64)), using
- concatenation of two codes [i] based on
- 2 times truncation [i] based on linear OA(4180, 222, F4, 95) (dual of [222, 42, 96]-code), using
- linear OA(4178, 221, F4, 92) (dual of [221, 43, 93]-code), using Gilbert–Varšamov bound and bm = 4178 > Vbs−1(k−1) = 115781 416850 000767 391926 036290 533873 431590 760235 965882 936709 978786 129243 959556 507163 365153 210543 001493 724617 [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(4180, 224, F4, 93) (dual of [224, 44, 94]-code) | [i] | Construction X with Varšamov Bound | |