Information on Result #684498
Linear OA(778, 5764831, F7, 11) (dual of [5764831, 5764753, 12]-code), using construction XX applied to Ce(10) ⊂ Ce(7) ⊂ Ce(5) 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(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(73, 28, F7, 2) (dual of [28, 25, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), 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(778, 5764831, F7, 2, 11) (dual of [(5764831, 2), 11529584, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(778, 5764831, F7, 3, 11) (dual of [(5764831, 3), 17294415, 12]-NRT-code) | [i] | ||
| 3 | Digital (67, 78, 5764831)-net over F7 | [i] | ||
| 4 | Linear OOA(778, 1921610, F7, 3, 11) (dual of [(1921610, 3), 5764752, 12]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(778, 1152966, F7, 11, 11) (dual of [(1152966, 11), 12682548, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |