Information on Result #1454313
Linear OOA(1695, 977725, F16, 2, 20) (dual of [(977725, 2), 1955355, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(1695, 977725, F16, 20) (dual of [977725, 977630, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(1695, 1048595, F16, 20) (dual of [1048595, 1048500, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(1693, 1048593, F16, 20) (dual of [1048593, 1048500, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(19) ⊂ Ce(16) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(1693, 1048593, F16, 20) (dual of [1048593, 1048500, 21]-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(1695, 195544, F16, 22, 20) (dual of [(195544, 22), 4301873, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |