Information on Result #700491

Linear OA(236, 47, F2, 16) (dual of [47, 11, 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]) 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(21, 6, F2, 1) (dual of [6, 5, 2]-code), using
  6. linear OA(25, 10, F2, 3) (dual of [10, 5, 4]-code or 10-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.

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Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(237, 48, F2, 17) (dual of [48, 11, 18]-code) [i]Adding a Parity Check Bit
2Linear OOA(236, 23, F2, 2, 16) (dual of [(23, 2), 10, 17]-NRT-code) [i]OOA Folding