Information on Result #1453289
Linear OOA(1649, 1048595, F16, 2, 10) (dual of [(1048595, 2), 2097141, 11]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(1649, 1048595, F16, 10) (dual of [1048595, 1048546, 11]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(1648, 1048593, F16, 10) (dual of [1048593, 1048545, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(1646, 1048576, F16, 10) (dual of [1048576, 1048530, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1631, 1048576, F16, 7) (dual of [1048576, 1048545, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(1648, 1048594, F16, 9) (dual of [1048594, 1048546, 10]-code), using Gilbert–Varšamov bound and bm = 1648 > Vbs−1(k−1) = 92908 148794 100743 465711 956012 023298 980908 357612 295446 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(1648, 1048593, F16, 10) (dual of [1048593, 1048545, 11]-code), 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(1649, 349531, F16, 14, 10) (dual of [(349531, 14), 4893385, 11]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |