Information on Result #1304005
Linear OA(2240, 570, F2, 52) (dual of [570, 330, 53]-code), using 4 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1) based on linear OA(2234, 560, F2, 52) (dual of [560, 326, 53]-code), using
- construction XX applied to C1 = C([461,0]), C2 = C([469,2]), C3 = C1 + C2 = C([469,0]), and C∩ = C1 ∩ C2 = C([461,2]) [i] based on
- linear OA(2208, 511, F2, 51) (dual of [511, 303, 52]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,0}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−42,−41,…,2}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2217, 511, F2, 53) (dual of [511, 294, 54]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,2}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−42,−41,…,0}, and designed minimum distance d ≥ |I|+1 = 44 [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(21, 10, F2, 1) (dual of [10, 9, 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: 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(2241, 571, F2, 53) (dual of [571, 330, 54]-code) | [i] | Adding a Parity Check Bit | |