Information on Result #700675

Linear OA(2139, 154, F2, 64) (dual of [154, 15, 65]-code), using construction XX applied to C1 = C({1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}), C2 = C([1,55]), C3 = C1 + C2 = C([1,47]), and C∩ = C1 ∩ C2 = C([1,63]) based on
  1. linear OA(2119, 127, F2, 62) (dual of [127, 8, 63]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}, and minimum distance d ≥ |{9,18,27,…,50}|+1 = 63 (BCH-bound) [i]
  2. linear OA(2119, 127, F2, 62) (dual of [127, 8, 63]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,55], and designed minimum distance d ≥ |I|+1 = 63 [i]
  3. linear OA(2126, 127, F2, 126) (dual of [127, 1, 127]-code or 127-arc in PG(125,2)), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,63], and designed minimum distance d ≥ |I|+1 = 127 [i]
  4. linear OA(2112, 127, F2, 54) (dual of [127, 15, 55]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 55 [i]
  5. linear OA(21, 8, F2, 1) (dual of [8, 7, 2]-code), using
  6. linear OA(212, 19, F2, 7) (dual of [19, 7, 8]-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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(2139, 154, F2, 63) (dual of [154, 15, 64]-code) [i]Strength Reduction
2Linear OA(2140, 155, F2, 65) (dual of [155, 15, 66]-code) [i]Adding a Parity Check Bit
3Linear OOA(2139, 77, F2, 2, 64) (dual of [(77, 2), 15, 65]-NRT-code) [i]OOA Folding
4Linear OOA(2139, 51, F2, 3, 64) (dual of [(51, 3), 14, 65]-NRT-code) [i]