Information on Result #1304391
Linear OA(3118, 925, F3, 26) (dual of [925, 807, 27]-code), using 170 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 1, 0, 0, 0, 1, 6 times 0, 1, 8 times 0, 1, 12 times 0, 1, 16 times 0, 1, 21 times 0, 1, 26 times 0, 1, 30 times 0, 1, 34 times 0) based on linear OA(3104, 741, F3, 26) (dual of [741, 637, 27]-code), using
- construction XX applied to C1 = C([340,364]), C2 = C([342,365]), C3 = C1 + C2 = C([342,364]), and C∩ = C1 ∩ C2 = C([340,365]) [i] based on
- 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 = {340,341,…,364}, and designed minimum distance d ≥ |I|+1 = 26 [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(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(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 = {342,343,…,364}, and designed minimum distance d ≥ |I|+1 = 24 [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(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
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(3118, 925, F3, 2, 26) (dual of [(925, 2), 1732, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3118, 925, F3, 3, 26) (dual of [(925, 3), 2657, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(3118, 925, F3, 4, 26) (dual of [(925, 4), 3582, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(3118, 925, F3, 5, 26) (dual of [(925, 5), 4507, 27]-NRT-code) | [i] | ||
| 5 | Digital (92, 118, 925)-net over F3 | [i] | ||