Information on Result #690863
Linear OA(969, 85, F9, 52) (dual of [85, 16, 53]-code), using construction XX applied to C1 = C([0,99]), C2 = C([1,103]), C3 = C1 + C2 = C([1,99]), and C∩ = C1 ∩ C2 = C([0,103]) based on
- 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(967, 80, F9, 51) (dual of [80, 13, 52]-code), using contraction [i] based on linear OA(9147, 160, F9, 103) (dual of [160, 13, 104]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,103], and designed minimum distance d ≥ |I|+1 = 104 [i]
- linear OA(968, 80, F9, 52) (dual of [80, 12, 53]-code), using contraction [i] based on linear OA(9148, 160, F9, 105) (dual of [160, 12, 106]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,103], and minimum distance d ≥ |{−1,0,…,103}|+1 = 106 (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(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(969, 85, F9, 51) (dual of [85, 16, 52]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(969, 85, F9, 50) (dual of [85, 16, 51]-code) | [i] | ||
| 3 | Linear OA(963, 79, F9, 46) (dual of [79, 16, 47]-code) | [i] | Truncation | |
| 4 | Linear OA(962, 78, F9, 45) (dual of [78, 16, 46]-code) | [i] | ||
| 5 | Linear OA(961, 77, F9, 44) (dual of [77, 16, 45]-code) | [i] | ||
| 6 | Linear OA(960, 76, F9, 43) (dual of [76, 16, 44]-code) | [i] | ||