Information on Result #701821
Linear OA(2122, 301, F2, 28) (dual of [301, 179, 29]-code), using construction XX applied to C1 = C([229,254]), C2 = C([235,2]), C3 = C1 + C2 = C([235,254]), and C∩ = C1 ∩ C2 = C([229,2]) based on
- linear OA(2100, 255, F2, 26) (dual of [255, 155, 27]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−26,−25,…,−1}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(285, 255, F2, 23) (dual of [255, 170, 24]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−20,−19,…,2}, and designed minimum distance d ≥ |I|+1 = 24 [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 = {−26,−25,…,2}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(276, 255, F2, 20) (dual of [255, 179, 21]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−20,−19,…,−1}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(212, 36, F2, 5) (dual of [36, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-code), 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(2123, 302, F2, 29) (dual of [302, 179, 30]-code) | [i] | Adding a Parity Check Bit | |