Information on Result #1304222
Linear OA(372, 273, F3, 20) (dual of [273, 201, 21]-code), using 19 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 7 times 0) based on linear OA(366, 248, F3, 20) (dual of [248, 182, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(366, 243, F3, 20) (dual of [243, 177, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(361, 243, F3, 19) (dual of [243, 182, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(30, 5, F3, 0) (dual of [5, 5, 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(372, 273, F3, 2, 20) (dual of [(273, 2), 474, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(372, 273, F3, 3, 20) (dual of [(273, 3), 747, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(372, 273, F3, 4, 20) (dual of [(273, 4), 1020, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(372, 273, F3, 5, 20) (dual of [(273, 5), 1293, 21]-NRT-code) | [i] | ||
| 5 | Digital (52, 72, 273)-net over F3 | [i] | ||