Information on Result #1313025
Linear OA(928, 1041, F9, 9) (dual of [1041, 1013, 10]-code), using 304 step Varšamov–Edel lengthening with (ri) = (1, 13 times 0, 1, 80 times 0, 1, 208 times 0) based on linear OA(925, 734, F9, 9) (dual of [734, 709, 10]-code), using
- construction XX applied to C1 = C([727,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([727,7]) [i] based on
- linear OA(922, 728, F9, 8) (dual of [728, 706, 9]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(922, 728, F9, 8) (dual of [728, 706, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(925, 728, F9, 9) (dual of [728, 703, 10]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(919, 728, F9, 7) (dual of [728, 709, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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(928, 1041, F9, 2, 9) (dual of [(1041, 2), 2054, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(928, 1041, F9, 3, 9) (dual of [(1041, 3), 3095, 10]-NRT-code) | [i] | ||
| 3 | Digital (19, 28, 1041)-net over F9 | [i] | ||
| 4 | Linear OOA(928, 520, F9, 2, 9) (dual of [(520, 2), 1012, 10]-NRT-code) | [i] | OOA Folding | |