Information on Result #1313840
Linear OA(1678, 4211, F16, 26) (dual of [4211, 4133, 27]-code), using 104 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 20 times 0, 1, 77 times 0) based on linear OA(1674, 4103, F16, 26) (dual of [4103, 4029, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- linear OA(1673, 4096, F16, 26) (dual of [4096, 4023, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(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(1678, 4211, F16, 2, 26) (dual of [(4211, 2), 8344, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (52, 78, 4211)-net over F16 | [i] | ||
| 3 | Linear OOA(1678, 2105, F16, 2, 26) (dual of [(2105, 2), 4132, 27]-NRT-code) | [i] | OOA Folding | |