Information on Result #2227982
Linear OA(384, 99, F3, 48) (dual of [99, 15, 49]-code), using 2 times truncation based on linear OA(386, 101, F3, 50) (dual of [101, 15, 51]-code), using
- construction XX applied to C1 = C([0,81]), C2 = C([1,99]), C3 = C1 + C2 = C([1,81]), and C∩ = C1 ∩ C2 = C([0,99]) [i] based on
- linear OA(366, 80, F3, 41) (dual of [80, 14, 42]-code), using contraction [i] based on linear OA(3146, 160, F3, 83) (dual of [160, 14, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,81], and minimum distance d ≥ |{−1,0,…,81}|+1 = 84 (BCH-bound) [i]
- linear OA(373, 80, F3, 49) (dual of [80, 7, 50]-code), using contraction [i] based on linear OA(3153, 160, F3, 99) (dual of [160, 7, 100]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,99], and designed minimum distance d ≥ |I|+1 = 100 [i]
- linear OA(374, 80, F3, 50) (dual of [80, 6, 51]-code), using contraction [i] based on linear OA(3154, 160, F3, 101) (dual of [160, 6, 102]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,99], and minimum distance d ≥ |{−1,0,…,99}|+1 = 102 (BCH-bound) [i]
- 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 narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,81], and designed minimum distance d ≥ |I|+1 = 82 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(312, 20, F3, 8) (dual of [20, 8, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(312, 24, F3, 8) (dual of [24, 12, 9]-code), using
- extended quadratic residue code Qe(24,3) [i]
- discarding factors / shortening the dual code based on linear OA(312, 24, F3, 8) (dual of [24, 12, 9]-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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(384, 49, F3, 2, 48) (dual of [(49, 2), 14, 49]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(384, 33, F3, 3, 48) (dual of [(33, 3), 15, 49]-NRT-code) | [i] | ||