Information on Result #690869
Linear OA(972, 90, F9, 51) (dual of [90, 18, 52]-code), using construction XX applied to C1 = C([0,87]), C2 = C([1,101]), C3 = C1 + C2 = C([1,87]), and C∩ = C1 ∩ C2 = C([0,101]) based on
- linear OA(963, 80, F9, 44) (dual of [80, 17, 45]-code), using contraction [i] based on linear OA(9143, 160, F9, 89) (dual of [160, 17, 90]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,87], and minimum distance d ≥ |{−1,0,…,87}|+1 = 90 (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(962, 80, F9, 43) (dual of [80, 18, 44]-code), using contraction [i] based on linear OA(9142, 160, F9, 87) (dual of [160, 18, 88]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,87], and designed minimum distance d ≥ |I|+1 = 88 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(96, 9, F9, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,9)), using
- Reed–Solomon code RS(3,9) [i]
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(972, 45, F9, 2, 51) (dual of [(45, 2), 18, 52]-NRT-code) | [i] | OOA Folding | |