Information on Result #1311550
Linear OA(744, 367, F7, 16) (dual of [367, 323, 17]-code), using 17 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 0, 1, 10 times 0) based on linear OA(740, 346, F7, 16) (dual of [346, 306, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(740, 343, F7, 16) (dual of [343, 303, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(737, 343, F7, 15) (dual of [343, 306, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 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(744, 367, F7, 2, 16) (dual of [(367, 2), 690, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(744, 367, F7, 3, 16) (dual of [(367, 3), 1057, 17]-NRT-code) | [i] | ||
| 3 | Digital (28, 44, 367)-net over F7 | [i] | ||
| 4 | Linear OOA(744, 183, F7, 2, 16) (dual of [(183, 2), 322, 17]-NRT-code) | [i] | OOA Folding | |