Information on Result #2175145
Linear OA(2200, 272, F2, 63) (dual of [272, 72, 64]-code), using adding a parity check bit based on linear OA(2199, 271, F2, 62) (dual of [271, 72, 63]-code), using
- construction XX applied to C([1,60]) ⊂ C([1,58]) ⊂ C([1,54]) [i] based on
- linear OA(2192, 255, F2, 62) (dual of [255, 63, 63]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,60], and minimum distance d ≥ 63 (sporadic result) [i]
- linear OA(2184, 255, F2, 60) (dual of [255, 71, 61]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,58], and minimum distance d ≥ 61 (sporadic result) [i]
- linear OA(2176, 255, F2, 54) (dual of [255, 79, 55]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [i]
- 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
- linear OA(25, 6, F2, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,2)), using
- dual of repetition code with length 6 [i]
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(2200, 272, F2, 62) (dual of [272, 72, 63]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2201, 273, F2, 63) (dual of [273, 72, 64]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2202, 274, F2, 63) (dual of [274, 72, 64]-code) | [i] | ||
| 4 | Linear OOA(2200, 136, F2, 2, 63) (dual of [(136, 2), 72, 64]-NRT-code) | [i] | OOA Folding | |