Information on Result #1107238
Linear OOA(345, 2391495, F3, 5, 5) (dual of [(2391495, 5), 11957430, 6]-NRT-code), using appending kth column based on linear OOA(345, 2391495, F3, 4, 5) (dual of [(2391495, 4), 9565935, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(32, 4, F3, 4, 2) (dual of [(4, 4), 14, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;14,3) [i]
- linear OOA(343, 2391491, F3, 4, 5) (dual of [(2391491, 4), 9565921, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 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 and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- linear OOA(32, 4, F3, 4, 2) (dual of [(4, 4), 14, 3]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3175, 5187696, F3, 5, 10) (dual of [(5187696, 5), 25938305, 11]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(3179, 5746935, F3, 5, 10) (dual of [(5746935, 5), 28734496, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(3191, 5187696, F3, 5, 11) (dual of [(5187696, 5), 25938289, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(3194, 5746935, F3, 5, 11) (dual of [(5746935, 5), 28734481, 12]-NRT-code) | [i] | ||
| 5 | Digital (40, 45, 2391495)-net over F3 | [i] | Net Defined by OOA | |