Information on Result #684468
Linear OA(774, 5764818, F7, 11) (dual of [5764818, 5764744, 12]-code), using construction X applied to Ce(10) ⊂ Ce(8) based on
- linear OA(773, 5764801, F7, 11) (dual of [5764801, 5764728, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(757, 5764801, F7, 9) (dual of [5764801, 5764744, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(71, 17, F7, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and 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(774, 4946339, F7, 2, 11) (dual of [(4946339, 2), 9892604, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(774, 4946339, F7, 3, 11) (dual of [(4946339, 3), 14838943, 12]-NRT-code) | [i] | ||
| 3 | Digital (63, 74, 4946339)-net over F7 | [i] | ||
| 4 | Linear OOA(774, 2882409, F7, 2, 11) (dual of [(2882409, 2), 5764744, 12]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(774, 1921606, F7, 3, 11) (dual of [(1921606, 3), 5764744, 12]-NRT-code) | [i] | ||
| 6 | Linear OOA(774, 1152963, F7, 11, 11) (dual of [(1152963, 11), 12682519, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |