Information on Result #701549
Linear OA(845, 70, F8, 30) (dual of [70, 25, 31]-code), using construction X applied to C({2,3,4,5,6,10,11,12,13,14,19}) ⊂ C({3,4,5,6,10,11,12,13,14,19}) based on
- linear OA(844, 65, F8, 30) (dual of [65, 21, 31]-code), using the cyclic code C(A) with length 65 | 84−1, defining set A = {2,3,4,5,6,10,11,12,13,14,19}, and minimum distance d ≥ |{−16,12,40,…,16}|+1 = 31 (BCH-bound) [i]
- linear OA(840, 65, F8, 28) (dual of [65, 25, 29]-code), using the cyclic code C(A) with length 65 | 84−1, defining set A = {3,4,5,6,10,11,12,13,14,19}, and minimum distance d ≥ |{12,40,3,…,−12}|+1 = 29 (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(845, 70, F8, 29) (dual of [70, 25, 30]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(847, 72, F8, 30) (dual of [72, 25, 31]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(844, 69, F8, 29) (dual of [69, 25, 30]-code) | [i] | Truncation | |
| 4 | Linear OA(851, 81, F8, 30) (dual of [81, 30, 31]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(852, 85, F8, 30) (dual of [85, 33, 31]-code) | [i] | ||
| 6 | Linear OA(853, 90, F8, 30) (dual of [90, 37, 31]-code) | [i] | ||
| 7 | Linear OOA(845, 35, F8, 2, 30) (dual of [(35, 2), 25, 31]-NRT-code) | [i] | OOA Folding | |