Information on Result #702004
Linear OA(2167, 273, F2, 49) (dual of [273, 106, 50]-code), using construction XX applied to C1 = C([253,44]), C2 = C([0,46]), C3 = C1 + C2 = C([0,44]), and C∩ = C1 ∩ C2 = C([253,46]) based on
- 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 = {−2,−1,…,44}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2157, 255, F2, 47) (dual of [255, 98, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2165, 255, F2, 49) (dual of [255, 90, 50]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,46}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2149, 255, F2, 45) (dual of [255, 106, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- 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
- linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code) (see above)
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(2166, 272, F2, 48) (dual of [272, 106, 49]-code) | [i] | Truncation | |
| 2 | Linear OOA(2167, 136, F2, 2, 49) (dual of [(136, 2), 105, 50]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2167, 91, F2, 3, 49) (dual of [(91, 3), 106, 50]-NRT-code) | [i] | ||