Information on Result #2677296
Linear OOA(3193, 1594340, F3, 3, 20) (dual of [(1594340, 3), 4782827, 21]-NRT-code), using 31 times duplication based on linear OOA(3192, 1594340, F3, 3, 20) (dual of [(1594340, 3), 4782828, 21]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3189, 1594339, F3, 3, 20) (dual of [(1594339, 3), 4782828, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3189, 4783017, F3, 20) (dual of [4783017, 4782828, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(3183, 4782969, F3, 20) (dual of [4782969, 4782786, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- OOA 3-folding [i] based on linear OA(3189, 4783017, F3, 20) (dual of [4783017, 4782828, 21]-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(3193, 1575141, F3, 4, 20) (dual of [(1575141, 4), 6300371, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3193, 1575141, F3, 5, 20) (dual of [(1575141, 5), 7875512, 21]-NRT-code) | [i] | ||
| 3 | Digital (173, 193, 1575141)-net over F3 | [i] | ||