Information on Result #689244
Linear OA(9129, 531456, F9, 24) (dual of [531456, 531327, 25]-code), using construction XX applied to Ce(23) ⊂ Ce(21) ⊂ Ce(20) based on
- linear OA(9127, 531441, F9, 24) (dual of [531441, 531314, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(9109, 531441, F9, 21) (dual of [531441, 531332, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(91, 14, F9, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(9129, 403372, F9, 2, 24) (dual of [(403372, 2), 806615, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9129, 403372, F9, 3, 24) (dual of [(403372, 3), 1209987, 25]-NRT-code) | [i] | ||
| 3 | Digital (105, 129, 403372)-net over F9 | [i] | ||
| 4 | Linear OOA(9129, 265728, F9, 2, 24) (dual of [(265728, 2), 531327, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(9129, 177152, F9, 3, 24) (dual of [(177152, 3), 531327, 25]-NRT-code) | [i] | ||
| 6 | Linear OOA(9129, 44288, F9, 24, 24) (dual of [(44288, 24), 1062783, 25]-NRT-code) | [i] | OA Folding and Stacking | |