Information on Result #1094565
Linear OOA(342, 797171, F3, 5, 5) (dual of [(797171, 5), 3985813, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(342, 797172, F3, 2, 5) (dual of [(797172, 2), 1594302, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(32, 4, F3, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;6,3) [i]
- linear OOA(340, 797168, F3, 2, 5) (dual of [(797168, 2), 1594296, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(340, 1594336, F3, 5) (dual of [1594336, 1594296, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(340, 1594323, F3, 5) (dual of [1594323, 1594283, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(327, 1594323, F3, 4) (dual of [1594323, 1594296, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 13, F3, 0) (dual of [13, 13, 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
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding [i] based on linear OA(340, 1594336, F3, 5) (dual of [1594336, 1594296, 6]-code), using
- linear OOA(32, 4, F3, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
Mode: Constructive and 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(3127, 1753764, F3, 5, 10) (dual of [(1753764, 5), 8768693, 11]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(3141, 1753767, F3, 5, 11) (dual of [(1753767, 5), 8768694, 12]-NRT-code) | [i] | ||
| 3 | Digital (37, 42, 797171)-net over F3 | [i] | Net Defined by OOA | |