Information on Result #684639
Linear OA(782, 117664, F7, 16) (dual of [117664, 117582, 17]-code), using construction X applied to Ce(15) ⊂ Ce(12) based on
- linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(767, 117649, F7, 13) (dual of [117649, 117582, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(73, 15, F7, 2) (dual of [15, 12, 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
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(782, 78119, F7, 2, 16) (dual of [(78119, 2), 156156, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(782, 78119, F7, 3, 16) (dual of [(78119, 3), 234275, 17]-NRT-code) | [i] | ||
| 3 | Digital (66, 82, 78119)-net over F7 | [i] | ||
| 4 | Linear OOA(782, 58832, F7, 2, 16) (dual of [(58832, 2), 117582, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(782, 39221, F7, 3, 16) (dual of [(39221, 3), 117581, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(782, 14708, F7, 16, 16) (dual of [(14708, 16), 235246, 17]-NRT-code) | [i] | OA Folding and Stacking | |