Information on Result #702385

Linear OA(2188, 558, F2, 41) (dual of [558, 370, 42]-code), using construction XX applied to C1 = C([505,30]), C2 = C([0,34]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([505,34]) based on
  1. linear OA(2163, 511, F2, 37) (dual of [511, 348, 38]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,30}, and designed minimum distance d ≥ |I|+1 = 38 [i]
  2. 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]
  3. linear OA(2172, 511, F2, 41) (dual of [511, 339, 42]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,34}, and designed minimum distance d ≥ |I|+1 = 42 [i]
  4. linear OA(2136, 511, F2, 31) (dual of [511, 375, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
  5. 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]
  6. linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), 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:

ResultThis
result
only		Method
1Linear OA(2187, 557, F2, 40) (dual of [557, 370, 41]-code) [i]Truncation
2Linear OOA(2188, 279, F2, 2, 41) (dual of [(279, 2), 370, 42]-NRT-code) [i]OOA Folding
3Linear OOA(2188, 186, F2, 3, 41) (dual of [(186, 3), 370, 42]-NRT-code) [i]
4Linear OOA(2188, 139, F2, 4, 41) (dual of [(139, 4), 368, 42]-NRT-code) [i]