Information on Result #701560
Linear OA(861, 70, F8, 48) (dual of [70, 9, 49]-code), using construction X applied to C([1,21]) ⊂ C({1,2,3,5,6,7,10,11,12,13,14,19,20,21}) based on
- linear OA(860, 65, F8, 48) (dual of [65, 5, 49]-code), using the narrow-sense BCH-code C(I) with length 65 | 84−1, defining interval I = [1,27], and minimum distance d ≥ |{−8,20,48,…,8}|+1 = 49 (BCH-bound) [i]
- linear OA(856, 65, F8, 46) (dual of [65, 9, 47]-code), using the cyclic code C(A) with length 65 | 84−1, defining set A = {1,2,3,5,6,7,10,11,12,13,14,19,20,21}, and minimum distance d ≥ |{−25,−21,−17,…,25}|+1 = 47 (BCH-bound) [i]
- linear OA(81, 5, F8, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(861, 70, F8, 47) (dual of [70, 9, 48]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(8131, 140, F8, 97) (dual of [140, 9, 98]-code) | [i] | Repeating Each Code Word | |
| 3 | Linear OA(8125, 134, F8, 94) (dual of [134, 9, 95]-code) | [i] | Juxtaposition | |
| 4 | Linear OA(8126, 135, F8, 95) (dual of [135, 9, 96]-code) | [i] | ||
| 5 | Linear OOA(861, 35, F8, 2, 48) (dual of [(35, 2), 9, 49]-NRT-code) | [i] | OOA Folding | |