Information on Result #701859

Linear OA(2111, 273, F2, 29) (dual of [273, 162, 30]-code), using construction XX applied to C1 = C([253,24]), C2 = C([0,26]), C3 = C1 + C2 = C([0,24]), and C∩ = C1 ∩ C2 = C([253,26]) based on
  1. linear OA(2101, 255, F2, 27) (dual of [255, 154, 28]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,24}, and designed minimum distance d ≥ |I|+1 = 28 [i]
  2. linear OA(2101, 255, F2, 27) (dual of [255, 154, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
  3. linear OA(2109, 255, F2, 29) (dual of [255, 146, 30]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,26}, and designed minimum distance d ≥ |I|+1 = 30 [i]
  4. linear OA(293, 255, F2, 25) (dual of [255, 162, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
  5. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
  6. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code) (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(2110, 272, F2, 28) (dual of [272, 162, 29]-code) [i]Truncation
2Linear OOA(2111, 136, F2, 2, 29) (dual of [(136, 2), 161, 30]-NRT-code) [i]OOA Folding
3Linear OOA(2111, 91, F2, 3, 29) (dual of [(91, 3), 162, 30]-NRT-code) [i]
4Linear OOA(2111, 68, F2, 4, 29) (dual of [(68, 4), 161, 30]-NRT-code) [i]
5Linear OOA(2111, 54, F2, 5, 29) (dual of [(54, 5), 159, 30]-NRT-code) [i]