Information on Result #702625
Linear OA(2256, 569, F2, 57) (dual of [569, 313, 58]-code), using construction XX applied to C1 = C([459,510]), C2 = C([465,4]), C3 = C1 + C2 = C([465,510]), and C∩ = C1 ∩ C2 = C([459,4]) based on
- linear OA(2216, 511, F2, 52) (dual of [511, 295, 53]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−52,−51,…,−1}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2217, 511, F2, 51) (dual of [511, 294, 52]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−46,−45,…,4}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2235, 511, F2, 57) (dual of [511, 276, 58]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−52,−51,…,4}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(2198, 511, F2, 46) (dual of [511, 313, 47]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−46,−45,…,−1}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(211, 29, F2, 5) (dual of [29, 18, 6]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- linear OA(210, 29, F2, 4) (dual of [29, 19, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), using
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33 | 210−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(210, 32, F2, 4) (dual of [32, 22, 5]-code), using
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(2255, 568, F2, 56) (dual of [568, 313, 57]-code) | [i] | Truncation | |