Information on Result #1314004
Linear OA(16109, 5232, F16, 36) (dual of [5232, 5123, 37]-code), using 1124 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 14 times 0, 1, 46 times 0, 1, 117 times 0, 1, 224 times 0, 1, 326 times 0, 1, 387 times 0) based on linear OA(16100, 4099, F16, 36) (dual of [4099, 3999, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- linear OA(16100, 4096, F16, 36) (dual of [4096, 3996, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- 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(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-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(16109, 5232, F16, 2, 36) (dual of [(5232, 2), 10355, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (73, 109, 5232)-net over F16 | [i] | ||
| 3 | Linear OOA(16109, 2616, F16, 2, 36) (dual of [(2616, 2), 5123, 37]-NRT-code) | [i] | OOA Folding | |