Information on Result #684809
Linear OA(749, 16825, F7, 11) (dual of [16825, 16776, 12]-code), using construction X applied to Ce(10) ⊂ Ce(7) based on
- 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(731, 16807, F7, 8) (dual of [16807, 16776, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(73, 18, F7, 2) (dual of [18, 15, 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(750, 16826, F7, 11) (dual of [16826, 16776, 12]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(749, 16825, F7, 2, 11) (dual of [(16825, 2), 33601, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(749, 16825, F7, 3, 11) (dual of [(16825, 3), 50426, 12]-NRT-code) | [i] | ||
| 4 | Digital (38, 49, 16825)-net over F7 | [i] | ||
| 5 | Linear OA(750, 16827, F7, 11) (dual of [16827, 16777, 12]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(751, 16829, F7, 11) (dual of [16829, 16778, 12]-code) | [i] | ||
| 7 | Linear OOA(749, 8412, F7, 2, 11) (dual of [(8412, 2), 16775, 12]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(749, 5608, F7, 3, 11) (dual of [(5608, 3), 16775, 12]-NRT-code) | [i] | ||
| 9 | Linear OOA(749, 3364, F7, 11, 11) (dual of [(3364, 11), 36955, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |