Information on Result #702291
Linear OA(2129, 532, F2, 28) (dual of [532, 403, 29]-code), using construction XX applied to C1 = C([509,24]), C2 = C([1,26]), C3 = C1 + C2 = C([1,24]), and C∩ = C1 ∩ C2 = C([509,26]) based on
- linear OA(2118, 511, F2, 27) (dual of [511, 393, 28]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,24}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2117, 511, F2, 26) (dual of [511, 394, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2127, 511, F2, 29) (dual of [511, 384, 30]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,26}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2108, 511, F2, 24) (dual of [511, 403, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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, 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 (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(2130, 533, F2, 29) (dual of [533, 403, 30]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2129, 266, F2, 2, 28) (dual of [(266, 2), 403, 29]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2129, 177, F2, 3, 28) (dual of [(177, 3), 402, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(2129, 133, F2, 4, 28) (dual of [(133, 4), 403, 29]-NRT-code) | [i] | ||