Information on Result #702566
Linear OA(2228, 543, F2, 53) (dual of [543, 315, 54]-code), using construction XX applied to C1 = C([461,0]), C2 = C([467,2]), C3 = C1 + C2 = C([467,0]), and C∩ = C1 ∩ C2 = C([461,2]) 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(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 = {−44,−43,…,2}, and designed minimum distance d ≥ |I|+1 = 48 [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(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 = {−44,−43,…,0}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(210, 22, F2, 5) (dual of [22, 12, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 24, F2, 5) (dual of [24, 14, 6]-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: 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(2227, 542, F2, 52) (dual of [542, 315, 53]-code) | [i] | Truncation | |
| 2 | Linear OOA(2228, 271, F2, 2, 53) (dual of [(271, 2), 314, 54]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2228, 181, F2, 3, 53) (dual of [(181, 3), 315, 54]-NRT-code) | [i] | ||