Information on Result #692108
Linear OA(16100, 4108, F16, 35) (dual of [4108, 4008, 36]-code), using construction X applied to Ce(34) ⊂ Ce(30) based on
- linear OA(1697, 4096, F16, 35) (dual of [4096, 3999, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(1688, 4096, F16, 31) (dual of [4096, 4008, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(163, 12, F16, 3) (dual of [12, 9, 4]-code or 12-arc in PG(2,16) or 12-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), 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 OOA(16100, 3577, F16, 2, 35) (dual of [(3577, 2), 7054, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
2 | Digital (65, 100, 3577)-net over F16 | [i] | ||
3 | Linear OOA(16100, 2054, F16, 2, 35) (dual of [(2054, 2), 4008, 36]-NRT-code) | [i] | OOA Folding |