Information on Result #1311461
Linear OA(727, 471, F7, 9) (dual of [471, 444, 10]-code), using 120 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 13 times 0, 1, 33 times 0, 1, 67 times 0) based on linear OA(722, 346, F7, 9) (dual of [346, 324, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(722, 343, F7, 9) (dual of [343, 321, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(719, 343, F7, 8) (dual of [343, 324, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(727, 471, F7, 2, 9) (dual of [(471, 2), 915, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(727, 471, F7, 3, 9) (dual of [(471, 3), 1386, 10]-NRT-code) | [i] | ||
| 3 | Digital (18, 27, 471)-net over F7 | [i] | ||
| 4 | Linear OOA(727, 235, F7, 2, 9) (dual of [(235, 2), 443, 10]-NRT-code) | [i] | OOA Folding | |