Information on Result #1452375
Linear OOA(9140, 6575, F9, 2, 39) (dual of [(6575, 2), 13010, 40]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(9140, 6575, F9, 39) (dual of [6575, 6435, 40]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9138, 6571, F9, 39) (dual of [6571, 6433, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(9137, 6562, F9, 39) (dual of [6562, 6425, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(9129, 6562, F9, 37) (dual of [6562, 6433, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (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([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(9138, 6573, F9, 38) (dual of [6573, 6435, 39]-code), using Gilbert–Varšamov bound and bm = 9138 > Vbs−1(k−1) = 306631 601467 269246 415836 279248 049964 720922 697007 489411 016616 623514 637615 953597 079742 957091 948579 527501 769598 485038 669800 687397 630433 [i]
- linear OA(90, 2, F9, 0) (dual of [2, 2, 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
- linear OA(9138, 6571, F9, 39) (dual of [6571, 6433, 40]-code), 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(9140, 3287, F9, 3, 39) (dual of [(3287, 3), 9721, 40]-NRT-code) | [i] | OOA Folding | |