Information on Result #2225226
Linear OA(2178, 268, F2, 54) (dual of [268, 90, 55]-code), using 1 times truncation based on linear OA(2179, 269, F2, 55) (dual of [269, 90, 56]-code), using
- construction XX applied to C1 = C([253,50]), C2 = C([0,52]), C3 = C1 + C2 = C([0,50]), and C∩ = C1 ∩ C2 = C([253,52]) [i] based on
- 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 = {−2,−1,…,50}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2169, 255, F2, 53) (dual of [255, 86, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(2177, 255, F2, 55) (dual of [255, 78, 56]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(2165, 255, F2, 51) (dual of [255, 90, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [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, 5, F2, 1) (dual of [5, 4, 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 (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 OOA(2178, 134, F2, 2, 54) (dual of [(134, 2), 90, 55]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2178, 89, F2, 3, 54) (dual of [(89, 3), 89, 55]-NRT-code) | [i] | ||