Information on Result #1304472
Linear OA(3122, 817, F3, 28) (dual of [817, 695, 29]-code), using 64 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 9 times 0, 1, 13 times 0, 1, 18 times 0) based on linear OA(3111, 742, F3, 28) (dual of [742, 631, 29]-code), using
- construction XX applied to C1 = C([342,367]), C2 = C([340,365]), C3 = C1 + C2 = C([342,365]), and C∩ = C1 ∩ C2 = C([340,367]) [i] based on
- linear OA(3103, 728, F3, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {342,343,…,367}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3103, 728, F3, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,365}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3109, 728, F3, 28) (dual of [728, 619, 29]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,367}, and designed minimum distance d ≥ |I|+1 = 29 [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 = {342,343,…,365}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-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(3122, 817, F3, 2, 28) (dual of [(817, 2), 1512, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3122, 817, F3, 3, 28) (dual of [(817, 3), 2329, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(3122, 817, F3, 4, 28) (dual of [(817, 4), 3146, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(3122, 817, F3, 5, 28) (dual of [(817, 5), 3963, 29]-NRT-code) | [i] | ||
| 5 | Digital (94, 122, 817)-net over F3 | [i] | ||