Information on Result #702235

Linear OA(2107, 546, F2, 22) (dual of [546, 439, 23]-code), using construction XX applied to C1 = C([507,16]), C2 = C([1,18]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C([507,18]) based on
  1. linear OA(291, 511, F2, 21) (dual of [511, 420, 22]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,16}, and designed minimum distance d ≥ |I|+1 = 22 [i]
  2. linear OA(281, 511, F2, 18) (dual of [511, 430, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. linear OA(2100, 511, F2, 23) (dual of [511, 411, 24]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
  4. linear OA(272, 511, F2, 16) (dual of [511, 439, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(2109, 548, F2, 22) (dual of [548, 439, 23]-code) [i]Code Embedding in Larger Space
2Linear OA(2108, 547, F2, 23) (dual of [547, 439, 24]-code) [i]Adding a Parity Check Bit
3Linear OOA(2107, 273, F2, 2, 22) (dual of [(273, 2), 439, 23]-NRT-code) [i]OOA Folding
4Linear OOA(2107, 182, F2, 3, 22) (dual of [(182, 3), 439, 23]-NRT-code) [i]
5Linear OOA(2107, 109, F2, 5, 22) (dual of [(109, 5), 438, 23]-NRT-code) [i]
6Linear OOA(2107, 91, F2, 6, 22) (dual of [(91, 6), 439, 23]-NRT-code) [i]