Information on Result #700628

Linear OA(291, 147, F2, 29) (dual of [147, 56, 30]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,63}), C2 = C([0,23]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,63}) based on
  1. linear OA(278, 127, F2, 25) (dual of [127, 49, 26]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,63}, and minimum distance d ≥ |{−2,−1,…,22}|+1 = 26 (BCH-bound) [i]
  2. linear OA(278, 127, F2, 27) (dual of [127, 49, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
  3. linear OA(285, 127, F2, 29) (dual of [127, 42, 30]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,63}, and minimum distance d ≥ |{−2,−1,…,26}|+1 = 30 (BCH-bound) [i]
  4. linear OA(271, 127, F2, 23) (dual of [127, 56, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
  5. linear OA(21, 8, F2, 1) (dual of [8, 7, 2]-code), using
  6. linear OA(25, 12, F2, 3) (dual of [12, 7, 4]-code or 12-cap in PG(4,2)), 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(290, 146, F2, 28) (dual of [146, 56, 29]-code) [i]Truncation
2Linear OOA(291, 73, F2, 2, 29) (dual of [(73, 2), 55, 30]-NRT-code) [i]OOA Folding
3Linear OOA(291, 49, F2, 3, 29) (dual of [(49, 3), 56, 30]-NRT-code) [i]