Information on Result #684659
Linear OA(770, 117670, F7, 13) (dual of [117670, 117600, 14]-code), using construction X applied to Ce(12) ⊂ Ce(9) based on
- 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(749, 117649, F7, 10) (dual of [117649, 117600, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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 OOA(770, 117670, F7, 2, 13) (dual of [(117670, 2), 235270, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(770, 117670, F7, 3, 13) (dual of [(117670, 3), 352940, 14]-NRT-code) | [i] | ||
| 3 | Digital (57, 70, 117670)-net over F7 | [i] | ||
| 4 | Linear OOA(770, 58835, F7, 2, 13) (dual of [(58835, 2), 117600, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(770, 39223, F7, 3, 13) (dual of [(39223, 3), 117599, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(770, 19611, F7, 13, 13) (dual of [(19611, 13), 254873, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |