Information on Result #702006
Linear OA(2185, 291, F2, 53) (dual of [291, 106, 54]-code), using construction XX applied to C1 = C([205,0]), C2 = C([211,2]), C3 = C1 + C2 = C([211,0]), and C∩ = C1 ∩ C2 = C([205,2]) based on
- linear OA(2165, 255, F2, 51) (dual of [255, 90, 52]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−50,−49,…,0}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2157, 255, F2, 47) (dual of [255, 98, 48]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−44,−43,…,2}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2173, 255, F2, 53) (dual of [255, 82, 54]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−50,−49,…,2}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2149, 255, F2, 45) (dual of [255, 106, 46]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−44,−43,…,0}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(211, 27, F2, 5) (dual of [27, 16, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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 OOA(2185, 97, F2, 3, 53) (dual of [(97, 3), 106, 54]-NRT-code) | [i] | OOA Folding | |