Information on Result #1302764
Linear OA(8116, 2097171, F8, 19) (dual of [2097171, 2097055, 20]-code), using construction X with Varšamov bound based on
- linear OA(8114, 2097168, F8, 19) (dual of [2097168, 2097054, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(8113, 2097153, F8, 19) (dual of [2097153, 2097040, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(899, 2097153, F8, 17) (dual of [2097153, 2097054, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 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([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(8114, 2097169, F8, 17) (dual of [2097169, 2097055, 18]-code), using Gilbert–Varšamov bound and bm = 8114 > Vbs−1(k−1) = 222359 775426 990529 116180 460400 886452 789952 807828 799577 230901 828404 603176 857741 667249 476104 837044 240384 [i]
- linear OA(81, 2, F8, 1) (dual of [2, 1, 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 (see above)
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(8116, 699057, F8, 3, 19) (dual of [(699057, 3), 2097055, 20]-NRT-code) | [i] | OOA Folding | |