Information on Result #1313250
Linear OA(986, 739, F9, 32) (dual of [739, 653, 33]-code), using 4 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0) based on linear OA(985, 734, F9, 32) (dual of [734, 649, 33]-code), using
- construction XX applied to C1 = C([727,29]), C2 = C([0,30]), C3 = C1 + C2 = C([0,29]), and C∩ = C1 ∩ C2 = C([727,30]) [i] based on
- linear OA(982, 728, F9, 31) (dual of [728, 646, 32]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,29}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(982, 728, F9, 31) (dual of [728, 646, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(985, 728, F9, 32) (dual of [728, 643, 33]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,30}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(979, 728, F9, 30) (dual of [728, 649, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code) (see above)
Mode: 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(986, 739, F9, 2, 32) (dual of [(739, 2), 1392, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(986, 739, F9, 3, 32) (dual of [(739, 3), 2131, 33]-NRT-code) | [i] | ||
| 3 | Digital (54, 86, 739)-net over F9 | [i] | ||