Information on Result #816667
Linear OOA(374, 45, F3, 2, 44) (dual of [(45, 2), 16, 45]-NRT-code), using OOA 2-folding based on linear OA(374, 90, F3, 44) (dual of [90, 16, 45]-code), using
- construction XX applied to C1 = C([0,79]), C2 = C([1,87]), C3 = C1 + C2 = C([1,79]), and C∩ = C1 ∩ C2 = C([0,87]) [i] based on
- linear OA(365, 80, F3, 40) (dual of [80, 15, 41]-code), using contraction [i] based on linear OA(3145, 160, F3, 81) (dual of [160, 15, 82]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,79], and minimum distance d ≥ |{−1,0,…,79}|+1 = 82 (BCH-bound) [i]
- linear OA(369, 80, F3, 43) (dual of [80, 11, 44]-code), using contraction [i] based on linear OA(3149, 160, F3, 87) (dual of [160, 11, 88]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,87], and designed minimum distance d ≥ |I|+1 = 88 [i]
- linear OA(370, 80, F3, 44) (dual of [80, 10, 45]-code), using contraction [i] based on linear OA(3150, 160, F3, 89) (dual of [160, 10, 90]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,87], and minimum distance d ≥ |{−1,0,…,87}|+1 = 90 (BCH-bound) [i]
- linear OA(364, 80, F3, 39) (dual of [80, 16, 40]-code), using contraction [i] based on linear OA(3144, 160, F3, 79) (dual of [160, 16, 80]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(34, 9, F3, 3) (dual of [9, 5, 4]-code or 9-cap in PG(3,3)), 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(374, 45, F3, 2, 43) (dual of [(45, 2), 16, 44]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(374, 45, F3, 2, 42) (dual of [(45, 2), 16, 43]-NRT-code) | [i] | ||
| 3 | Linear OOA(376, 46, F3, 2, 44) (dual of [(46, 2), 16, 45]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 4 | Linear OOA(375, 45, F3, 2, 44) (dual of [(45, 2), 15, 45]-NRT-code) | [i] | OOA Duplication | |
| 5 | Linear OOA(370, 43, F3, 2, 40) (dual of [(43, 2), 16, 41]-NRT-code) | [i] | Truncation for OOAs | |
| 6 | Linear OOA(369, 42, F3, 2, 39) (dual of [(42, 2), 15, 40]-NRT-code) | [i] | ||
| 7 | Linear OOA(368, 42, F3, 2, 38) (dual of [(42, 2), 16, 39]-NRT-code) | [i] | ||