Information on Result #702259

Linear OA(2125, 546, F2, 26) (dual of [546, 421, 27]-code), using construction XX applied to C1 = C([507,20]), C2 = C([1,22]), C3 = C1 + C2 = C([1,20]), and C∩ = C1 ∩ C2 = C([507,22]) based on
  1. linear OA(2109, 511, F2, 25) (dual of [511, 402, 26]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,20}, and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(299, 511, F2, 22) (dual of [511, 412, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  3. linear OA(2118, 511, F2, 27) (dual of [511, 393, 28]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [i]
  4. linear OA(290, 511, F2, 20) (dual of [511, 421, 21]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  5. linear OA(26, 25, F2, 3) (dual of [25, 19, 4]-code or 25-cap in PG(5,2)), using
  6. linear OA(21, 10, F2, 1) (dual of [10, 9, 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(2127, 548, F2, 26) (dual of [548, 421, 27]-code) [i]Code Embedding in Larger Space
2Linear OA(2126, 547, F2, 27) (dual of [547, 421, 28]-code) [i]Adding a Parity Check Bit
3Linear OOA(2125, 273, F2, 2, 26) (dual of [(273, 2), 421, 27]-NRT-code) [i]OOA Folding
4Linear OOA(2125, 182, F2, 3, 26) (dual of [(182, 3), 421, 27]-NRT-code) [i]
5Linear OOA(2125, 109, F2, 5, 26) (dual of [(109, 5), 420, 27]-NRT-code) [i]