Information on Result #684787
Linear OA(739, 16820, F7, 9) (dual of [16820, 16781, 10]-code), using construction X applied to Ce(8) ⊂ Ce(5) based on
- linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(726, 16807, F7, 6) (dual of [16807, 16781, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(73, 13, F7, 2) (dual of [13, 10, 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(739, 16820, F7, 2, 9) (dual of [(16820, 2), 33601, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(739, 16820, F7, 3, 9) (dual of [(16820, 3), 50421, 10]-NRT-code) | [i] | ||
| 3 | Digital (30, 39, 16820)-net over F7 | [i] | ||
| 4 | Linear OOA(739, 8410, F7, 2, 9) (dual of [(8410, 2), 16781, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(739, 5606, F7, 3, 9) (dual of [(5606, 3), 16779, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(739, 4204, F7, 9, 9) (dual of [(4204, 9), 37797, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |