Information on Result #1301422
Linear OA(569, 136, F5, 32) (dual of [136, 67, 33]-code), using construction X with Varšamov bound based on
- linear OA(563, 127, F5, 32) (dual of [127, 64, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(562, 126, F5, 32) (dual of [126, 64, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(562, 125, F5, 32) (dual of [125, 63, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(561, 125, F5, 31) (dual of [125, 64, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(562, 126, F5, 32) (dual of [126, 64, 33]-code), using
- linear OA(563, 130, F5, 28) (dual of [130, 67, 29]-code), using Gilbert–Varšamov bound and bm = 563 > Vbs−1(k−1) = 91 579863 405740 614762 894611 694365 358210 823685 [i]
- linear OA(53, 6, F5, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,5) or 6-cap in PG(2,5)), using
- extended Reed–Solomon code RSe(3,5) [i]
- oval in PG(2, 5) [i]
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(570, 138, F5, 32) (dual of [138, 68, 33]-code) | [i] | Construction X with Varšamov Bound | |