Information on Result #701623
Linear OA(4953, 60, F49, 49) (dual of [60, 7, 50]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24}), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C([0,24]) based on
- linear OA(4947, 50, F49, 47) (dual of [50, 3, 48]-code or 50-arc in PG(46,49)), using the cyclic code C(A) with length 50 | 492−1, defining set A = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24}, and minimum distance d ≥ |{−19,−16,−13,…,19}|+1 = 48 (BCH-bound) [i]
- linear OA(4945, 50, F49, 45) (dual of [50, 5, 46]-code or 50-arc in PG(44,49)), using the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- linear OA(4949, 50, F49, 49) (dual of [50, 1, 50]-code or 50-arc in PG(48,49)), using the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,24], and minimum distance d ≥ |{−2,21,44,…,2}|+1 = 50 (BCH-bound) [i]
- linear OA(4943, 50, F49, 43) (dual of [50, 7, 44]-code or 50-arc in PG(42,49)), using the expurgated narrow-sense BCH-code C(I) with length 50 | 492−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(493, 7, F49, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,49) or 7-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- linear OA(491, 3, F49, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), using
- Reed–Solomon code RS(48,49) [i]
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), using
Mode: Constructive and 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 OA(4952, 59, F49, 48) (dual of [59, 7, 49]-code) | [i] | Truncation | |