Information on Result #690871
Linear OA(975, 100, F9, 50) (dual of [100, 25, 51]-code), using construction XX applied to C1 = C([0,79]), C2 = C([1,99]), C3 = C1 + C2 = C([1,79]), and C∩ = C1 ∩ C2 = C([0,99]) 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(964, 80, F9, 49) (dual of [80, 16, 50]-code), using contraction [i] based on linear OA(9144, 160, F9, 99) (dual of [160, 16, 100]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,99], and designed minimum distance d ≥ |I|+1 = 100 [i]
- linear OA(965, 80, F9, 50) (dual of [80, 15, 51]-code), using contraction [i] based on linear OA(9145, 160, F9, 101) (dual of [160, 15, 102]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,99], and minimum distance d ≥ |{−1,0,…,99}|+1 = 102 (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(910, 19, F9, 9) (dual of [19, 9, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- extended quadratic residue code Qe(20,9) [i]
- discarding factors / shortening the dual code based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-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(975, 100, F9, 49) (dual of [100, 25, 50]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(975, 100, F9, 48) (dual of [100, 25, 49]-code) | [i] | ||
| 3 | Linear OA(975, 100, F9, 47) (dual of [100, 25, 48]-code) | [i] | ||
| 4 | Linear OA(973, 98, F9, 48) (dual of [98, 25, 49]-code) | [i] | Truncation | |
| 5 | Linear OA(972, 97, F9, 47) (dual of [97, 25, 48]-code) | [i] | ||
| 6 | Linear OA(971, 96, F9, 46) (dual of [96, 25, 47]-code) | [i] | ||
| 7 | Linear OA(970, 95, F9, 45) (dual of [95, 25, 46]-code) | [i] | ||
| 8 | Linear OOA(975, 50, F9, 2, 50) (dual of [(50, 2), 25, 51]-NRT-code) | [i] | OOA Folding | |