Information on Result #702421
Linear OA(2197, 564, F2, 43) (dual of [564, 367, 44]-code), using construction XX applied to C1 = C([507,34]), C2 = C([1,38]), C3 = C1 + C2 = C([1,34]), and C∩ = C1 ∩ C2 = C([507,38]) based on
- linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,34}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2162, 511, F2, 38) (dual of [511, 349, 39]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,38}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2144, 511, F2, 34) (dual of [511, 367, 35]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- 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
- linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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(2197, 564, F2, 42) (dual of [564, 367, 43]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2196, 563, F2, 42) (dual of [563, 367, 43]-code) | [i] | Truncation | |
| 3 | Linear OOA(2197, 141, F2, 4, 43) (dual of [(141, 4), 367, 44]-NRT-code) | [i] | OOA Folding | |