Information on Result #690884
Linear OA(960, 85, F9, 42) (dual of [85, 25, 43]-code), using construction XX applied to C1 = C([0,79]), C2 = C([1,83]), C3 = C1 + C2 = C([1,79]), and C∩ = C1 ∩ C2 = C([0,83]) based on
- linear OA(956, 80, F9, 40) (dual of [80, 24, 41]-code), using contraction [i] based on linear OA(9136, 160, F9, 81) (dual of [160, 24, 82]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,79], and minimum distance d ≥ |{−1,0,…,79}|+1 = 82 (BCH-bound) [i]
- linear OA(958, 80, F9, 41) (dual of [80, 22, 42]-code), using contraction [i] based on linear OA(9138, 160, F9, 83) (dual of [160, 22, 84]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,83], and designed minimum distance d ≥ |I|+1 = 84 [i]
- linear OA(959, 80, F9, 42) (dual of [80, 21, 43]-code), using contraction [i] based on linear OA(9139, 160, F9, 85) (dual of [160, 21, 86]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,83], and minimum distance d ≥ |{−1,0,…,83}|+1 = 86 (BCH-bound) [i]
- linear OA(955, 80, F9, 39) (dual of [80, 25, 40]-code), using contraction [i] based on linear OA(9135, 160, F9, 79) (dual of [160, 25, 80]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(91, 4, F9, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- Reed–Solomon code RS(8,9) [i]
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-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 OA(960, 85, F9, 41) (dual of [85, 25, 42]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(959, 84, F9, 41) (dual of [84, 25, 42]-code) | [i] | Truncation | |
| 3 | Linear OA(958, 83, F9, 40) (dual of [83, 25, 41]-code) | [i] | ||
| 4 | Linear OA(954, 79, F9, 36) (dual of [79, 25, 37]-code) | [i] | ||
| 5 | Linear OA(953, 78, F9, 35) (dual of [78, 25, 36]-code) | [i] | ||