Information on Result #684780
Linear OA(757, 16818, F7, 13) (dual of [16818, 16761, 14]-code), using construction X applied to Ce(12) ⊂ Ce(10) based on
- linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 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(757, 16406, F7, 2, 13) (dual of [(16406, 2), 32755, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(757, 16406, F7, 3, 13) (dual of [(16406, 3), 49161, 14]-NRT-code) | [i] | ||
| 3 | Digital (44, 57, 16406)-net over F7 | [i] | ||
| 4 | Linear OOA(757, 8409, F7, 2, 13) (dual of [(8409, 2), 16761, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(757, 5606, F7, 3, 13) (dual of [(5606, 3), 16761, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(757, 2802, F7, 13, 13) (dual of [(2802, 13), 36369, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |