Information on Result #1304191
Linear OA(381, 781, F3, 18) (dual of [781, 700, 19]-code), using 33 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 8 times 0, 1, 12 times 0) based on linear OA(373, 740, F3, 18) (dual of [740, 667, 19]-code), using
- construction XX applied to C1 = C([727,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([727,16]) [i] based on
- linear OA(367, 728, F3, 17) (dual of [728, 661, 18]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [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(373, 728, F3, 18) (dual of [728, 655, 19]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(361, 728, F3, 16) (dual of [728, 667, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [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(381, 781, F3, 2, 18) (dual of [(781, 2), 1481, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(381, 781, F3, 3, 18) (dual of [(781, 3), 2262, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(381, 781, F3, 4, 18) (dual of [(781, 4), 3043, 19]-NRT-code) | [i] | ||
| 4 | Linear OOA(381, 781, F3, 5, 18) (dual of [(781, 5), 3824, 19]-NRT-code) | [i] | ||
| 5 | Digital (63, 81, 781)-net over F3 | [i] | ||