Information on Result #690868
Linear OA(974, 94, F9, 51) (dual of [94, 20, 52]-code), using construction XX applied to C1 = C([0,85]), C2 = C([1,101]), C3 = C1 + C2 = C([1,85]), and C∩ = C1 ∩ C2 = C([0,101]) based on
- linear OA(961, 80, F9, 43) (dual of [80, 19, 44]-code), using contraction [i] based on linear OA(9141, 160, F9, 87) (dual of [160, 19, 88]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,85], and minimum distance d ≥ |{−1,0,…,85}|+1 = 88 (BCH-bound) [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 narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,101], and designed minimum distance d ≥ |I|+1 = 102 [i]
- linear OA(966, 80, F9, 51) (dual of [80, 14, 52]-code), using contraction [i] based on linear OA(9146, 160, F9, 103) (dual of [160, 14, 104]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,101], and minimum distance d ≥ |{−1,0,…,101}|+1 = 104 (BCH-bound) [i]
- linear OA(960, 80, F9, 42) (dual of [80, 20, 43]-code), using contraction [i] based on linear OA(9140, 160, F9, 85) (dual of [160, 20, 86]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,85], and designed minimum distance d ≥ |I|+1 = 86 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(98, 13, F9, 7) (dual of [13, 5, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(98, 18, F9, 7) (dual of [18, 10, 8]-code), using
- 2 times truncation [i] based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- extended quadratic residue code Qe(20,9) [i]
- 2 times truncation [i] based on linear OA(910, 20, F9, 9) (dual of [20, 10, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(98, 18, F9, 7) (dual of [18, 10, 8]-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(974, 47, F9, 2, 51) (dual of [(47, 2), 20, 52]-NRT-code) | [i] | OOA Folding | |