Information on Result #1299312
Linear OA(3209, 2231, F3, 42) (dual of [2231, 2022, 43]-code), using construction X with Varšamov bound based on
- linear OA(3205, 2224, F3, 42) (dual of [2224, 2019, 43]-code), using
- construction X applied to C([0,21]) ⊂ C([0,18]) [i] based on
- linear OA(3197, 2188, F3, 43) (dual of [2188, 1991, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(3169, 2188, F3, 37) (dual of [2188, 2019, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2188 | 314−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(38, 36, F3, 4) (dual of [36, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to C([0,21]) ⊂ C([0,18]) [i] based on
- linear OA(3205, 2227, F3, 40) (dual of [2227, 2022, 41]-code), using Gilbert–Varšamov bound and bm = 3205 > Vbs−1(k−1) = 695893 031622 332623 144743 597239 941726 368616 334287 517802 940391 087869 483390 047799 537175 927797 468617 [i]
- linear OA(31, 4, F3, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-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
None.