Information on Result #702573
Linear OA(2252, 579, F2, 54) (dual of [579, 327, 55]-code), using construction XX applied to C1 = C([461,510]), C2 = C([469,4]), C3 = C1 + C2 = C([469,510]), and C∩ = C1 ∩ C2 = C([461,4]) based on
- linear OA(2207, 511, F2, 50) (dual of [511, 304, 51]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,−1}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−42,−41,…,4}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,4}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2180, 511, F2, 42) (dual of [511, 331, 43]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−42,−41,…,−1}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(216, 39, F2, 6) (dual of [39, 23, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(216, 42, F2, 6) (dual of [42, 26, 7]-code), using
- extracting embedded orthogonal array [i] based on digital (10, 16, 42)-net over F2, using
- discarding factors / shortening the dual code based on linear OA(216, 42, F2, 6) (dual of [42, 26, 7]-code), using
- linear OA(210, 29, F2, 4) (dual of [29, 19, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-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(2254, 581, F2, 54) (dual of [581, 327, 55]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2255, 582, F2, 54) (dual of [582, 327, 55]-code) | [i] | ||
| 3 | Linear OA(2256, 583, F2, 54) (dual of [583, 327, 55]-code) | [i] | ||
| 4 | Linear OA(2253, 580, F2, 55) (dual of [580, 327, 56]-code) | [i] | Adding a Parity Check Bit | |
| 5 | Linear OOA(2252, 193, F2, 3, 54) (dual of [(193, 3), 327, 55]-NRT-code) | [i] | OOA Folding | |