Information on Result #704376
Linear OA(3106, 763, F3, 25) (dual of [763, 657, 26]-code), using construction XX applied to C1 = C([722,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([722,18]) based on
- linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,16}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(373, 728, F3, 19) (dual of [728, 655, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(397, 728, F3, 25) (dual of [728, 631, 26]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,18}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(367, 728, F3, 17) (dual of [728, 661, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(38, 28, F3, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by construction Y1) [i] based on
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and 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(3106, 690, F3, 2, 25) (dual of [(690, 2), 1274, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3106, 690, F3, 3, 25) (dual of [(690, 3), 1964, 26]-NRT-code) | [i] | ||
| 3 | Linear OOA(3106, 690, F3, 4, 25) (dual of [(690, 4), 2654, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(3106, 690, F3, 5, 25) (dual of [(690, 5), 3344, 26]-NRT-code) | [i] | ||
| 5 | Digital (81, 106, 690)-net over F3 | [i] | ||
| 6 | Linear OOA(3106, 381, F3, 2, 25) (dual of [(381, 2), 656, 26]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3106, 254, F3, 3, 25) (dual of [(254, 3), 656, 26]-NRT-code) | [i] | ||