Information on Result #1313156
Linear OA(968, 1019, F9, 23) (dual of [1019, 951, 24]-code), using 278 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 11 times 0, 1, 30 times 0, 1, 57 times 0, 1, 78 times 0, 1, 93 times 0) based on linear OA(961, 734, F9, 23) (dual of [734, 673, 24]-code), using
- construction XX applied to C1 = C([727,20]), C2 = C([0,21]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([727,21]) [i] based on
- linear OA(958, 728, F9, 22) (dual of [728, 670, 23]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,20}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(958, 728, F9, 22) (dual of [728, 670, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(961, 728, F9, 23) (dual of [728, 667, 24]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,21}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(955, 728, F9, 21) (dual of [728, 673, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [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(968, 1019, F9, 2, 23) (dual of [(1019, 2), 1970, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(968, 1019, F9, 3, 23) (dual of [(1019, 3), 2989, 24]-NRT-code) | [i] | ||
| 3 | Digital (45, 68, 1019)-net over F9 | [i] | ||