Information on Result #702925

Linear OA(2208, 1070, F2, 41) (dual of [1070, 862, 42]-code), using construction XX applied to C1 = C([1019,32]), C2 = C([0,36]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([1019,36]) based on
  1. linear OA(2181, 1023, F2, 37) (dual of [1023, 842, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,32}, and designed minimum distance d ≥ |I|+1 = 38 [i]
  2. linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
  3. linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,36}, and designed minimum distance d ≥ |I|+1 = 42 [i]
  4. linear OA(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
  5. linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)), using
  6. linear OA(26, 21, F2, 3) (dual of [21, 15, 4]-code or 21-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:

ResultThis
result
only		Method
1Linear OA(2207, 1069, F2, 40) (dual of [1069, 862, 41]-code) [i]Truncation
2Linear OOA(2208, 535, F2, 2, 41) (dual of [(535, 2), 862, 42]-NRT-code) [i]OOA Folding
3Linear OOA(2208, 356, F2, 3, 41) (dual of [(356, 3), 860, 42]-NRT-code) [i]
4Linear OOA(2208, 267, F2, 4, 41) (dual of [(267, 4), 860, 42]-NRT-code) [i]
5Linear OOA(2208, 214, F2, 5, 41) (dual of [(214, 5), 862, 42]-NRT-code) [i]
6Linear OOA(2208, 178, F2, 6, 41) (dual of [(178, 6), 860, 42]-NRT-code) [i]