Information on Result #703040

Linear OA(2258, 1076, F2, 50) (dual of [1076, 818, 51]-code), using construction XX applied to C1 = C([1019,42]), C2 = C([1,46]), C3 = C1 + C2 = C([1,42]), and C∩ = C1 ∩ C2 = C([1019,46]) based on
  1. linear OA(2226, 1023, F2, 47) (dual of [1023, 797, 48]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
  2. linear OA(2225, 1023, F2, 46) (dual of [1023, 798, 47]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
  3. linear OA(2246, 1023, F2, 51) (dual of [1023, 777, 52]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,46}, and designed minimum distance d ≥ |I|+1 = 52 [i]
  4. linear OA(2205, 1023, F2, 42) (dual of [1023, 818, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
  5. linear OA(26, 27, F2, 3) (dual of [27, 21, 4]-code or 27-cap in PG(5,2)), using
  6. linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-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(2260, 1078, F2, 50) (dual of [1078, 818, 51]-code) [i]Code Embedding in Larger Space
2Linear OA(2259, 1077, F2, 51) (dual of [1077, 818, 52]-code) [i]Adding a Parity Check Bit
3Linear OOA(2258, 538, F2, 2, 50) (dual of [(538, 2), 818, 51]-NRT-code) [i]OOA Folding
4Linear OOA(2258, 269, F2, 4, 50) (dual of [(269, 4), 818, 51]-NRT-code) [i]
5Linear OOA(2258, 215, F2, 5, 50) (dual of [(215, 5), 817, 51]-NRT-code) [i]