Information on Result #702998
Linear OA(2221, 1049, F2, 45) (dual of [1049, 828, 46]-code), using construction XX applied to C1 = C([1021,40]), C2 = C([1,42]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([1021,42]) based on
- 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 = {−2,−1,…,40}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2205, 1023, F2, 42) (dual of [1023, 818, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2216, 1023, F2, 45) (dual of [1023, 807, 46]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,42}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2195, 1023, F2, 40) (dual of [1023, 828, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- Hamming code H(4,2) [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(2221, 1049, F2, 44) (dual of [1049, 828, 45]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2220, 1048, F2, 44) (dual of [1048, 828, 45]-code) | [i] | Truncation | |