Information on Result #702284

Linear OA(2134, 545, F2, 29) (dual of [545, 411, 30]-code), using construction XX applied to C1 = C([507,22]), C2 = C([0,24]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([507,24]) based on
  1. 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]
  2. linear OA(2109, 511, F2, 25) (dual of [511, 402, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
  3. linear OA(2127, 511, F2, 29) (dual of [511, 384, 30]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [i]
  4. linear OA(2100, 511, F2, 23) (dual of [511, 411, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
  5. linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-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(2133, 544, F2, 28) (dual of [544, 411, 29]-code) [i]Truncation
2Linear OOA(2134, 272, F2, 2, 29) (dual of [(272, 2), 410, 30]-NRT-code) [i]OOA Folding
3Linear OOA(2134, 181, F2, 3, 29) (dual of [(181, 3), 409, 30]-NRT-code) [i]
4Linear OOA(2134, 136, F2, 4, 29) (dual of [(136, 4), 410, 30]-NRT-code) [i]
5Linear OOA(2134, 109, F2, 5, 29) (dual of [(109, 5), 411, 30]-NRT-code) [i]