Information on Result #1304303
Linear OA(3103, 821, F3, 23) (dual of [821, 718, 24]-code), using 69 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 11 times 0, 1, 14 times 0, 1, 20 times 0) based on linear OA(392, 741, F3, 23) (dual of [741, 649, 24]-code), using
- construction XX applied to C1 = C([343,364]), C2 = C([345,365]), C3 = C1 + C2 = C([345,364]), and C∩ = C1 ∩ C2 = C([343,365]) [i] based on
- linear OA(385, 728, F3, 22) (dual of [728, 643, 23]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {343,344,…,364}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(385, 728, F3, 21) (dual of [728, 643, 22]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {345,346,…,365}, and designed minimum distance d ≥ |I|+1 = 22 [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 = {343,344,…,365}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(379, 728, F3, 20) (dual of [728, 649, 21]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {345,346,…,364}, and designed minimum distance d ≥ |I|+1 = 21 [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(3103, 821, F3, 2, 23) (dual of [(821, 2), 1539, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3103, 821, F3, 3, 23) (dual of [(821, 3), 2360, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(3103, 821, F3, 4, 23) (dual of [(821, 4), 3181, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(3103, 821, F3, 5, 23) (dual of [(821, 5), 4002, 24]-NRT-code) | [i] | ||
| 5 | Digital (80, 103, 821)-net over F3 | [i] | ||