Information on Result #1303354
Linear OA(999, 6573, F9, 27) (dual of [6573, 6474, 28]-code), using construction X with Varšamov bound based on
- linear OA(998, 6571, F9, 27) (dual of [6571, 6473, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(997, 6562, F9, 27) (dual of [6562, 6465, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(989, 6562, F9, 25) (dual of [6562, 6473, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(998, 6572, F9, 26) (dual of [6572, 6474, 27]-code), using Gilbert–Varšamov bound and bm = 998 > Vbs−1(k−1) = 642 311279 648027 383432 106219 116785 536272 196654 627827 804563 939633 261225 456648 603622 208106 440985 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(999, 6573, F9, 2, 27) (dual of [(6573, 2), 13047, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(999, 6573, F9, 3, 27) (dual of [(6573, 3), 19620, 28]-NRT-code) | [i] | ||
| 3 | Digital (72, 99, 6573)-net over F9 | [i] | ||