Information on Result #702434

Linear OA(2193, 559, F2, 43) (dual of [559, 366, 44]-code), using construction XX applied to C1 = C([507,34]), C2 = C([0,38]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([507,38]) based on
  1. 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]
  2. linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
  3. 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]
  4. linear OA(2145, 511, F2, 35) (dual of [511, 366, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
  5. linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
  6. linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)) (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:

ResultThis
result
only		Method
1Linear OA(2192, 558, F2, 42) (dual of [558, 366, 43]-code) [i]Truncation
2Linear OA(2199, 567, F2, 42) (dual of [567, 368, 43]-code) [i]Construction X with VarÅ¡amov Bound
3Linear OA(2200, 569, F2, 42) (dual of [569, 369, 43]-code) [i]
4Linear OOA(2193, 279, F2, 2, 43) (dual of [(279, 2), 365, 44]-NRT-code) [i]OOA Folding
5Linear OOA(2193, 186, F2, 3, 43) (dual of [(186, 3), 365, 44]-NRT-code) [i]
6Linear OOA(2193, 139, F2, 4, 43) (dual of [(139, 4), 363, 44]-NRT-code) [i]
7Linear OOA(2193, 111, F2, 5, 43) (dual of [(111, 5), 362, 44]-NRT-code) [i]