Information on Result #672356

Linear OA(2178, 524320, F2, 19) (dual of [524320, 524142, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
  1. linear OA(2172, 524288, F2, 19) (dual of [524288, 524116, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(2134, 524288, F2, 15) (dual of [524288, 524154, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  3. linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(2177, 524319, F2, 18) (dual of [524319, 524142, 19]-code) [i]Truncation
2Linear OOA(2178, 262160, F2, 2, 19) (dual of [(262160, 2), 524142, 20]-NRT-code) [i]OOA Folding
3Linear OOA(2178, 174773, F2, 3, 19) (dual of [(174773, 3), 524141, 20]-NRT-code) [i]
4Linear OOA(2178, 131080, F2, 4, 19) (dual of [(131080, 4), 524142, 20]-NRT-code) [i]
5Linear OOA(2178, 104864, F2, 5, 19) (dual of [(104864, 5), 524142, 20]-NRT-code) [i]
6Linear OOA(2178, 87386, F2, 6, 19) (dual of [(87386, 6), 524138, 20]-NRT-code) [i]
7Linear OOA(2178, 74902, F2, 7, 19) (dual of [(74902, 7), 524136, 20]-NRT-code) [i]
8Linear OOA(2178, 65540, F2, 8, 19) (dual of [(65540, 8), 524142, 20]-NRT-code) [i]
9Linear OOA(2178, 58257, F2, 19, 19) (dual of [(58257, 19), 1106705, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row