Information on Result #1304332
Linear OA(3106, 796, F3, 24) (dual of [796, 690, 25]-code), using 47 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 11 times 0, 1, 15 times 0) based on linear OA(397, 740, F3, 24) (dual of [740, 643, 25]-code), using
- construction XX applied to C1 = C([727,21]), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C([727,22]) [i] 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 = {−1,0,…,21}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(397, 728, F3, 24) (dual of [728, 631, 25]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,22}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(385, 728, F3, 22) (dual of [728, 643, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(30, 6, F3, 0) (dual of [6, 6, 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(3106, 796, F3, 2, 24) (dual of [(796, 2), 1486, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3106, 796, F3, 3, 24) (dual of [(796, 3), 2282, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(3106, 796, F3, 4, 24) (dual of [(796, 4), 3078, 25]-NRT-code) | [i] | ||
| 4 | Linear OOA(3106, 796, F3, 5, 24) (dual of [(796, 5), 3874, 25]-NRT-code) | [i] | ||
| 5 | Digital (82, 106, 796)-net over F3 | [i] | ||