Information on Result #1313072
Linear OA(949, 1061, F9, 16) (dual of [1061, 1012, 17]-code), using 321 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 22 times 0, 1, 56 times 0, 1, 98 times 0, 1, 135 times 0) based on linear OA(943, 734, F9, 16) (dual of [734, 691, 17]-code), using
- construction XX applied to C1 = C([727,13]), C2 = C([0,14]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([727,14]) [i] based on
- linear OA(940, 728, F9, 15) (dual of [728, 688, 16]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,13}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(940, 728, F9, 15) (dual of [728, 688, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(943, 728, F9, 16) (dual of [728, 685, 17]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(937, 728, F9, 14) (dual of [728, 691, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [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(949, 1061, F9, 2, 16) (dual of [(1061, 2), 2073, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(949, 1061, F9, 3, 16) (dual of [(1061, 3), 3134, 17]-NRT-code) | [i] | ||
| 3 | Digital (33, 49, 1061)-net over F9 | [i] | ||
| 4 | Linear OOA(949, 530, F9, 2, 16) (dual of [(530, 2), 1011, 17]-NRT-code) | [i] | OOA Folding | |