Information on Result #702939
Linear OA(2223, 1082, F2, 43) (dual of [1082, 859, 44]-code), using construction XX applied to C1 = C([985,0]), C2 = C([991,4]), C3 = C1 + C2 = C([991,0]), and C∩ = C1 ∩ C2 = C([985,4]) based on
- linear OA(2186, 1023, F2, 39) (dual of [1023, 837, 40]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−38,−37,…,0}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2181, 1023, F2, 37) (dual of [1023, 842, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−32,−31,…,4}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2206, 1023, F2, 43) (dual of [1023, 817, 44]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−38,−37,…,4}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−32,−31,…,0}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33 | 210−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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(2222, 1081, F2, 42) (dual of [1081, 859, 43]-code) | [i] | Truncation | |
| 2 | Linear OOA(2223, 541, F2, 2, 43) (dual of [(541, 2), 859, 44]-NRT-code) | [i] | OOA Folding | |