Information on Result #1117577
Linear OOA(3149, 956604, F3, 5, 15) (dual of [(956604, 5), 4782871, 16]-NRT-code), using (u, u+v)-construction based on
- linear OOA(37, 4, F3, 5, 7) (dual of [(4, 5), 13, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;13,3) [i]
- linear OOA(3142, 956600, F3, 5, 15) (dual of [(956600, 5), 4782858, 16]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3142, 4783000, F3, 15) (dual of [4783000, 4782858, 16]-code), using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(3141, 4782970, F3, 15) (dual of [4782970, 4782829, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- 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(329, 30, F3, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
- dual of repetition code with length 30 [i]
- linear OA(31, 30, F3, 1) (dual of [30, 29, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to C([0,7]) ⊂ C([0,6]) [i] based on
- OOA 5-folding [i] based on linear OA(3142, 4783000, F3, 15) (dual of [4783000, 4782858, 16]-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(3206, 1913208, F3, 5, 15) (dual of [(1913208, 5), 9565834, 16]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |