Information on Result #689545
Linear OA(9138, 59062, F9, 31) (dual of [59062, 58924, 32]-code), using construction XX applied to Ce(30) ⊂ Ce(28) ⊂ Ce(27) based on
- linear OA(9136, 59049, F9, 31) (dual of [59049, 58913, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(9126, 59049, F9, 29) (dual of [59049, 58923, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(91, 12, F9, 1) (dual of [12, 11, 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(9138, 46973, F9, 2, 31) (dual of [(46973, 2), 93808, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9138, 46973, F9, 3, 31) (dual of [(46973, 3), 140781, 32]-NRT-code) | [i] | ||
| 3 | Digital (107, 138, 46973)-net over F9 | [i] | ||
| 4 | Linear OOA(9138, 29531, F9, 2, 31) (dual of [(29531, 2), 58924, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(9138, 19687, F9, 3, 31) (dual of [(19687, 3), 58923, 32]-NRT-code) | [i] | ||