Information on Result #1313612
Linear OA(1631, 4327, F16, 10) (dual of [4327, 4296, 11]-code), using 222 step Varšamov–Edel lengthening with (ri) = (1, 15 times 0, 1, 205 times 0) based on linear OA(1629, 4103, F16, 10) (dual of [4103, 4074, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(1628, 4096, F16, 10) (dual of [4096, 4068, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1622, 4096, F16, 8) (dual of [4096, 4074, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(161, 7, F16, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(1631, 4327, F16, 2, 10) (dual of [(4327, 2), 8623, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (21, 31, 4327)-net over F16 | [i] | ||
| 3 | Linear OOA(1631, 2163, F16, 2, 10) (dual of [(2163, 2), 4295, 11]-NRT-code) | [i] | OOA Folding | |