Information on Result #952336
Linear OOA(3120, 1594335, F3, 3, 13) (dual of [(1594335, 3), 4782885, 14]-NRT-code), using OOA 3-folding based on linear OA(3120, 4783005, F3, 13) (dual of [4783005, 4782885, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3119, 4783004, F3, 13) (dual of [4783004, 4782885, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(3113, 4782970, F3, 13) (dual of [4782970, 4782857, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(385, 4782970, F3, 9) (dual of [4782970, 4782885, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(36, 34, F3, 3) (dual of [34, 28, 4]-code or 34-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [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(3120, 1594335, F3, 4, 13) (dual of [(1594335, 4), 6377220, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3120, 1594335, F3, 5, 13) (dual of [(1594335, 5), 7971555, 14]-NRT-code) | [i] | ||
| 3 | Digital (107, 120, 1594335)-net over F3 | [i] | ||