Information on Result #731573
Linear OA(1656, 131082, F16, 14) (dual of [131082, 131026, 15]-code), using trace code based on linear OA(25628, 65541, F256, 14) (dual of [65541, 65513, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and 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 OA(1657, 131083, F16, 14) (dual of [131083, 131026, 15]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1656, 116448, F16, 2, 14) (dual of [(116448, 2), 232840, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (42, 56, 116448)-net over F16 | [i] | ||
| 4 | Linear OA(1657, 131084, F16, 14) (dual of [131084, 131027, 15]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(1656, 65541, F16, 2, 14) (dual of [(65541, 2), 131026, 15]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(1656, 18726, F16, 14, 14) (dual of [(18726, 14), 262108, 15]-NRT-code) | [i] | OA Folding and Stacking | |