Information on Result #1313817
Linear OA(1678, 5369, F16, 25) (dual of [5369, 5291, 26]-code), using 1262 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 16 times 0, 1, 64 times 0, 1, 200 times 0, 1, 411 times 0, 1, 562 times 0) based on linear OA(1670, 4099, F16, 25) (dual of [4099, 4029, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(1670, 4096, F16, 25) (dual of [4096, 4026, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(1667, 4096, F16, 24) (dual of [4096, 4029, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 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
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(1678, 5369, F16, 2, 25) (dual of [(5369, 2), 10660, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (53, 78, 5369)-net over F16 | [i] | ||
| 3 | Linear OOA(1678, 2684, F16, 2, 25) (dual of [(2684, 2), 5290, 26]-NRT-code) | [i] | OOA Folding | |