Information on Result #2175200
Linear OA(2236, 562, F2, 53) (dual of [562, 326, 54]-code), using adding a parity check bit based on linear OA(2235, 561, F2, 52) (dual of [561, 326, 53]-code), using
- construction XX applied to C1 = C([461,510]), C2 = C([469,2]), C3 = C1 + C2 = C([469,510]), and C∩ = C1 ∩ C2 = C([461,2]) [i] 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(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(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(217, 39, F2, 7) (dual of [39, 22, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(217, 40, F2, 7) (dual of [40, 23, 8]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(217, 40, F2, 7) (dual of [40, 23, 8]-code), using
- 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(2236, 562, F2, 52) (dual of [562, 326, 53]-code) | [i] | Strength Reduction | |
| 2 | Linear OOA(2236, 281, F2, 2, 53) (dual of [(281, 2), 326, 54]-NRT-code) | [i] | OOA Folding | |