Information on Result #702280

Linear OA(2139, 559, F2, 29) (dual of [559, 420, 30]-code), using construction XX applied to C1 = C([507,20]), C2 = C([0,24]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([507,24]) 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(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(291, 511, F2, 21) (dual of [511, 420, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [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(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)) (see above)

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(2138, 558, F2, 28) (dual of [558, 420, 29]-code) [i]Truncation
2Linear OOA(2139, 279, F2, 2, 29) (dual of [(279, 2), 419, 30]-NRT-code) [i]OOA Folding
3Linear OOA(2139, 186, F2, 3, 29) (dual of [(186, 3), 419, 30]-NRT-code) [i]
4Linear OOA(2139, 139, F2, 4, 29) (dual of [(139, 4), 417, 30]-NRT-code) [i]
5Linear OOA(2139, 111, F2, 5, 29) (dual of [(111, 5), 416, 30]-NRT-code) [i]