Information on Result #731727

Linear OA(2231, 240, F2, 112) (dual of [240, 9, 113]-code), using juxtaposition based on
  1. linear OA(235, 44, F2, 16) (dual of [44, 9, 17]-code), using
    • discarding factors / shortening the dual code based on linear OA(235, 45, F2, 16) (dual of [45, 10, 17]-code), using
      • construction XX applied to C1 = C({1,3,5,7,15}), C2 = C([1,11]), C3 = C1 + C2 = C([1,7]), and C∩ = C1 ∩ C2 = C([1,15]) [i] based on
        1. linear OA(225, 31, F2, 14) (dual of [31, 6, 15]-code), using the primitive cyclic code C(A) with length 31 = 25−1, defining set A = {1,3,5,7,15}, and minimum distance d ≥ |{5,10,15,…,8}|+1 = 15 (BCH-bound) [i]
        2. linear OA(225, 31, F2, 14) (dual of [31, 6, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 15 [i]
        3. linear OA(230, 31, F2, 30) (dual of [31, 1, 31]-code or 31-arc in PG(29,2)), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 31 [i]
        4. linear OA(220, 31, F2, 10) (dual of [31, 11, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 11 [i]
        5. linear OA(24, 8, F2, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
        6. linear OA(21, 6, F2, 1) (dual of [6, 5, 2]-code), using
  2. linear OA(2187, 196, F2, 95) (dual of [196, 9, 96]-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

None.