Information on Result #684500
Linear OA(759, 5764812, F7, 9) (dual of [5764812, 5764753, 10]-code), using construction XX applied to Ce(8) ⊂ Ce(7) ⊂ Ce(5) based on
- 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(749, 5764801, F7, 8) (dual of [5764801, 5764752, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(741, 5764801, F7, 6) (dual of [5764801, 5764760, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(70, 9, F7, 0) (dual of [9, 9, 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
- linear OA(71, 2, F7, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(759, 5662497, F7, 2, 9) (dual of [(5662497, 2), 11324935, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(759, 5662497, F7, 3, 9) (dual of [(5662497, 3), 16987432, 10]-NRT-code) | [i] | ||
| 3 | Digital (50, 59, 5662497)-net over F7 | [i] | ||
| 4 | Linear OOA(759, 2882406, F7, 2, 9) (dual of [(2882406, 2), 5764753, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(759, 1921604, F7, 3, 9) (dual of [(1921604, 3), 5764753, 10]-NRT-code) | [i] | ||