Information on Result #692158
Linear OA(1653, 4112, F16, 18) (dual of [4112, 4059, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(1649, 4096, F16, 18) (dual of [4096, 4047, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1637, 4096, F16, 13) (dual of [4096, 4059, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
- Reed–Solomon code RS(12,16) [i]
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(1653, 3706, F16, 2, 18) (dual of [(3706, 2), 7359, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (35, 53, 3706)-net over F16 | [i] | ||
| 3 | Linear OOA(1653, 2056, F16, 2, 18) (dual of [(2056, 2), 4059, 19]-NRT-code) | [i] | OOA Folding | |