Information on Result #702495

Linear OA(2206, 546, F2, 46) (dual of [546, 340, 47]-code), using construction XX applied to C1 = C([507,40]), C2 = C([1,42]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([507,42]) based on
  1. linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,40}, and designed minimum distance d ≥ |I|+1 = 46 [i]
  2. linear OA(2180, 511, F2, 42) (dual of [511, 331, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
  3. linear OA(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
  4. linear OA(2171, 511, F2, 40) (dual of [511, 340, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(2208, 548, F2, 46) (dual of [548, 340, 47]-code) [i]Code Embedding in Larger Space
2Linear OA(2207, 547, F2, 47) (dual of [547, 340, 48]-code) [i]Adding a Parity Check Bit
3Linear OOA(2206, 273, F2, 2, 46) (dual of [(273, 2), 340, 47]-NRT-code) [i]OOA Folding
4Linear OOA(2206, 182, F2, 3, 46) (dual of [(182, 3), 340, 47]-NRT-code) [i]
5Linear OOA(2206, 109, F2, 5, 46) (dual of [(109, 5), 339, 47]-NRT-code) [i]