Information on Result #702584

Linear OA(2223, 535, F2, 53) (dual of [535, 312, 54]-code), using construction XX applied to C1 = C([461,0]), C2 = C([465,2]), C3 = C1 + C2 = C([465,0]), and C∩ = C1 ∩ C2 = C([461,2]) based on
  1. linear OA(2208, 511, F2, 51) (dual of [511, 303, 52]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,0}, and designed minimum distance d ≥ |I|+1 = 52 [i]
  2. linear OA(2208, 511, F2, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−46,−45,…,2}, and designed minimum distance d ≥ |I|+1 = 50 [i]
  3. linear OA(2217, 511, F2, 53) (dual of [511, 294, 54]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−50,−49,…,2}, and designed minimum distance d ≥ |I|+1 = 54 [i]
  4. 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 = {−46,−45,…,0}, and designed minimum distance d ≥ |I|+1 = 48 [i]
  5. linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), 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(2222, 534, F2, 52) (dual of [534, 312, 53]-code) [i]Truncation
2Linear OOA(2223, 267, F2, 2, 53) (dual of [(267, 2), 311, 54]-NRT-code) [i]OOA Folding
3Linear OOA(2223, 178, F2, 3, 53) (dual of [(178, 3), 311, 54]-NRT-code) [i]
4Linear OOA(2223, 133, F2, 4, 53) (dual of [(133, 4), 309, 54]-NRT-code) [i]
5Linear OOA(2223, 107, F2, 5, 53) (dual of [(107, 5), 312, 54]-NRT-code) [i]