Information on Result #684661
Linear OA(758, 117670, F7, 11) (dual of [117670, 117612, 12]-code), using construction X applied to Ce(10) ⊂ Ce(7) based on
- linear OA(755, 117649, F7, 11) (dual of [117649, 117594, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(737, 117649, F7, 8) (dual of [117649, 117612, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(73, 21, F7, 2) (dual of [21, 18, 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 OA(759, 117671, F7, 11) (dual of [117671, 117612, 12]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(758, 117670, F7, 2, 11) (dual of [(117670, 2), 235282, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(758, 117670, F7, 3, 11) (dual of [(117670, 3), 352952, 12]-NRT-code) | [i] | ||
| 4 | Digital (47, 58, 117670)-net over F7 | [i] | ||
| 5 | Linear OA(759, 117672, F7, 11) (dual of [117672, 117613, 12]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(760, 117674, F7, 11) (dual of [117674, 117614, 12]-code) | [i] | ||
| 7 | Linear OOA(758, 58835, F7, 2, 11) (dual of [(58835, 2), 117612, 12]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(758, 39223, F7, 3, 11) (dual of [(39223, 3), 117611, 12]-NRT-code) | [i] | ||
| 9 | Linear OOA(758, 23533, F7, 11, 11) (dual of [(23533, 11), 258805, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |