Information on Result #692081
Linear OA(1677, 4103, F16, 27) (dual of [4103, 4026, 28]-code), using construction X applied to Ce(26) ⊂ Ce(24) based on
- linear OA(1676, 4096, F16, 27) (dual of [4096, 4020, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(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: 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(1696, 4168, F16, 27) (dual of [4168, 4072, 28]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(1697, 4170, F16, 27) (dual of [4170, 4073, 28]-code) | [i] | ||
| 3 | Linear OOA(1677, 3092, F16, 2, 27) (dual of [(3092, 2), 6107, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (50, 77, 3092)-net over F16 | [i] | ||
| 5 | Linear OA(1680, 4138, F16, 27) (dual of [4138, 4058, 28]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(1681, 4235, F16, 27) (dual of [4235, 4154, 28]-code) | [i] | ||
| 7 | Linear OA(1682, 4494, F16, 27) (dual of [4494, 4412, 28]-code) | [i] | ||
| 8 | Linear OOA(1677, 2051, F16, 2, 27) (dual of [(2051, 2), 4025, 28]-NRT-code) | [i] | OOA Folding | |