Information on Result #2174957
Linear OA(2112, 275, F2, 29) (dual of [275, 163, 30]-code), using adding a parity check bit based on linear OA(2111, 274, F2, 28) (dual of [274, 163, 29]-code), using
- construction XX applied to C1 = C([253,24]), C2 = C([1,26]), C3 = C1 + C2 = C([1,24]), and C∩ = C1 ∩ C2 = C([253,26]) [i] based on
- linear OA(2101, 255, F2, 27) (dual of [255, 154, 28]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,24}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2100, 255, F2, 26) (dual of [255, 155, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2109, 255, F2, 29) (dual of [255, 146, 30]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,26}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(292, 255, F2, 24) (dual of [255, 163, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(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 (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(2112, 275, F2, 28) (dual of [275, 163, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2113, 276, F2, 29) (dual of [276, 163, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OOA(2112, 137, F2, 2, 29) (dual of [(137, 2), 162, 30]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2112, 55, F2, 5, 29) (dual of [(55, 5), 163, 30]-NRT-code) | [i] | ||