Information on Result #1311581
Linear OA(767, 4816, F7, 17) (dual of [4816, 4749, 18]-code), using 9 step Varšamov–Edel lengthening with (ri) = (1, 8 times 0) based on linear OA(766, 4806, F7, 17) (dual of [4806, 4740, 18]-code), using
- trace code [i] based on linear OA(4933, 2403, F49, 17) (dual of [2403, 2370, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(4931, 2401, F49, 16) (dual of [2401, 2370, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
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(767, 4816, F7, 2, 17) (dual of [(4816, 2), 9565, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(767, 4816, F7, 3, 17) (dual of [(4816, 3), 14381, 18]-NRT-code) | [i] | ||
| 3 | Digital (50, 67, 4816)-net over F7 | [i] | ||
| 4 | Linear OOA(767, 2408, F7, 2, 17) (dual of [(2408, 2), 4749, 18]-NRT-code) | [i] | OOA Folding | |