Information on Result #702757

Linear OA(2108, 1061, F2, 20) (dual of [1061, 953, 21]-code), using construction XX applied to C1 = C([1019,14]), C2 = C([1,16]), C3 = C1 + C2 = C([1,14]), and C∩ = C1 ∩ C2 = C([1019,16]) based on
  1. linear OA(291, 1023, F2, 19) (dual of [1023, 932, 20]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,14}, and designed minimum distance d ≥ |I|+1 = 20 [i]
  2. linear OA(280, 1023, F2, 16) (dual of [1023, 943, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(2101, 1023, F2, 21) (dual of [1023, 922, 22]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,16}, and designed minimum distance d ≥ |I|+1 = 22 [i]
  4. linear OA(270, 1023, F2, 14) (dual of [1023, 953, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(21, 11, F2, 1) (dual of [11, 10, 2]-code), 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(2109, 1062, F2, 21) (dual of [1062, 953, 22]-code) [i]Adding a Parity Check Bit
2Linear OOA(2108, 530, F2, 2, 20) (dual of [(530, 2), 952, 21]-NRT-code) [i]OOA Folding
3Linear OOA(2108, 265, F2, 4, 20) (dual of [(265, 4), 952, 21]-NRT-code) [i]
4Linear OOA(2108, 212, F2, 5, 20) (dual of [(212, 5), 952, 21]-NRT-code) [i]