Information on Result #813191
Linear OOA(3148, 2391509, F3, 2, 15) (dual of [(2391509, 2), 4782870, 16]-NRT-code), using OOA 2-folding based on linear OA(3148, 4783018, F3, 15) (dual of [4783018, 4782870, 16]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3147, 4783017, F3, 15) (dual of [4783017, 4782870, 16]-code), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
- linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(15) ⊂ Ce(10) [i] based on
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(3148, 1687733, F3, 3, 15) (dual of [(1687733, 3), 5063051, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3148, 1687733, F3, 4, 15) (dual of [(1687733, 4), 6750784, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(3148, 1687733, F3, 5, 15) (dual of [(1687733, 5), 8438517, 16]-NRT-code) | [i] | ||
| 4 | Digital (133, 148, 1687733)-net over F3 | [i] | ||