Information on Result #700528

Linear OA(240, 84, F2, 13) (dual of [84, 44, 14]-code), using construction XX applied to C1 = C({0,1,3,5,31}), C2 = C([0,9]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,31}) based on
  1. linear OA(225, 63, F2, 9) (dual of [63, 38, 10]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,3,5,31}, and minimum distance d ≥ |{−2,−1,…,6}|+1 = 10 (BCH-bound) [i]
  2. linear OA(228, 63, F2, 11) (dual of [63, 35, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(234, 63, F2, 13) (dual of [63, 29, 14]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,3,5,7,9,31}, and minimum distance d ≥ |{−2,−1,…,10}|+1 = 14 (BCH-bound) [i]
  4. linear OA(219, 63, F2, 7) (dual of [63, 44, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
  5. linear OA(21, 7, F2, 1) (dual of [7, 6, 2]-code), using
  6. linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-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(239, 83, F2, 12) (dual of [83, 44, 13]-code) [i]Truncation
2Linear OOA(240, 42, F2, 2, 13) (dual of [(42, 2), 44, 14]-NRT-code) [i]OOA Folding
3Linear OOA(240, 28, F2, 3, 13) (dual of [(28, 3), 44, 14]-NRT-code) [i]