Information on Result #672626

Linear OA(2122, 32785, F2, 16) (dual of [32785, 32663, 17]-code), using construction X4 applied to C([0,16]) ⊂ C([1,14]) based on
  1. linear OA(2121, 32767, F2, 17) (dual of [32767, 32646, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(2105, 32767, F2, 14) (dual of [32767, 32662, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  3. linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
  4. linear OA(21, 18, F2, 1) (dual of [18, 17, 2]-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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(2124, 32787, F2, 16) (dual of [32787, 32663, 17]-code) [i]Code Embedding in Larger Space
2Linear OA(2125, 32788, F2, 16) (dual of [32788, 32663, 17]-code) [i]
3Linear OA(2123, 32786, F2, 17) (dual of [32786, 32663, 18]-code) [i]Adding a Parity Check Bit
4Linear OOA(2122, 16392, F2, 2, 16) (dual of [(16392, 2), 32662, 17]-NRT-code) [i]OOA Folding
5Linear OOA(2122, 10928, F2, 3, 16) (dual of [(10928, 3), 32662, 17]-NRT-code) [i]
6Linear OOA(2122, 8196, F2, 4, 16) (dual of [(8196, 4), 32662, 17]-NRT-code) [i]
7Linear OOA(2122, 6557, F2, 5, 16) (dual of [(6557, 5), 32663, 17]-NRT-code) [i]
8Linear OOA(2122, 5464, F2, 6, 16) (dual of [(5464, 6), 32662, 17]-NRT-code) [i]
9Linear OOA(2122, 4098, F2, 8, 16) (dual of [(4098, 8), 32662, 17]-NRT-code) [i]
10Linear OOA(2122, 4098, F2, 16, 16) (dual of [(4098, 16), 65446, 17]-NRT-code) [i]OA Folding and Stacking