Information on Result #690862
Linear OA(976, 94, F9, 52) (dual of [94, 18, 53]-code), using construction XX applied to C1 = C([0,87]), C2 = C([1,103]), C3 = C1 + C2 = C([1,87]), and C∩ = C1 ∩ C2 = C([0,103]) 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(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(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(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(976, 47, F9, 2, 52) (dual of [(47, 2), 18, 53]-NRT-code) | [i] | OOA Folding | |