Information on Result #1313582
Linear OA(1617, 4130, F16, 6) (dual of [4130, 4113, 7]-code), using 30 step Varšamov–Edel lengthening with (ri) = (1, 29 times 0) based on linear OA(1616, 4099, F16, 6) (dual of [4099, 4083, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(1616, 4096, F16, 6) (dual of [4096, 4080, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1613, 4096, F16, 5) (dual of [4096, 4083, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(1617, 4130, F16, 2, 6) (dual of [(4130, 2), 8243, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (11, 17, 4130)-net over F16 | [i] | ||
| 3 | Linear OOA(1617, 2065, F16, 2, 6) (dual of [(2065, 2), 4113, 7]-NRT-code) | [i] | OOA Folding | |