Information on Result #1559396
Linear OOA(8173, 32782, F8, 3, 39) (dual of [(32782, 3), 98173, 40]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8173, 32782, F8, 39) (dual of [32782, 32609, 40]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8172, 32780, F8, 39) (dual of [32780, 32608, 40]-code), using
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(8171, 32769, F8, 39) (dual of [32769, 32598, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(8161, 32769, F8, 37) (dual of [32769, 32608, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 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
- construction X applied to C([0,19]) ⊂ C([0,18]) [i] based on
- linear OA(8172, 32781, F8, 38) (dual of [32781, 32609, 39]-code), using Gilbert–Varšamov bound and bm = 8172 > Vbs−1(k−1) = 158002 837722 696415 200496 489368 392196 128584 473538 409103 557247 051352 292079 574764 023486 788235 321225 392689 869176 156818 784330 849868 547358 793554 260285 212005 545984 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(8172, 32780, F8, 39) (dual of [32780, 32608, 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(8173, 4683, F8, 45, 39) (dual of [(4683, 45), 210562, 40]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |