Information on Result #689844
Linear OA(9115, 6572, F9, 32) (dual of [6572, 6457, 33]-code), using construction XX applied to Ce(31) ⊂ Ce(29) ⊂ Ce(28) based on
- linear OA(9113, 6561, F9, 32) (dual of [6561, 6448, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(9105, 6561, F9, 30) (dual of [6561, 6456, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(9101, 6561, F9, 29) (dual of [6561, 6460, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(91, 10, F9, 1) (dual of [10, 9, 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(9115, 6348, F9, 2, 32) (dual of [(6348, 2), 12581, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9115, 6348, F9, 3, 32) (dual of [(6348, 3), 18929, 33]-NRT-code) | [i] | ||
| 3 | Digital (83, 115, 6348)-net over F9 | [i] | ||
| 4 | Linear OOA(9115, 3286, F9, 2, 32) (dual of [(3286, 2), 6457, 33]-NRT-code) | [i] | OOA Folding | |