Information on Result #1313045
Linear OA(938, 1223, F9, 12) (dual of [1223, 1185, 13]-code), using 482 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 11 times 0, 1, 32 times 0, 1, 79 times 0, 1, 144 times 0, 1, 207 times 0) based on linear OA(931, 734, F9, 12) (dual of [734, 703, 13]-code), using
- construction XX applied to C1 = C([727,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([727,10]) [i] based on
- linear OA(928, 728, F9, 11) (dual of [728, 700, 12]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(928, 728, F9, 11) (dual of [728, 700, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(931, 728, F9, 12) (dual of [728, 697, 13]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(925, 728, F9, 10) (dual of [728, 703, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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(938, 1223, F9, 2, 12) (dual of [(1223, 2), 2408, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(938, 1223, F9, 3, 12) (dual of [(1223, 3), 3631, 13]-NRT-code) | [i] | ||
| 3 | Digital (26, 38, 1223)-net over F9 | [i] | ||
| 4 | Linear OOA(938, 611, F9, 2, 12) (dual of [(611, 2), 1184, 13]-NRT-code) | [i] | OOA Folding | |