Information on Result #691676

Linear OA(16113, 1048613, F16, 23) (dual of [1048613, 1048500, 24]-code), using construction X applied to Ce(22) ⊂ Ce(16) based on
  1. linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  2. linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(167, 37, F16, 5) (dual of [37, 30, 6]-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(16114, 1048614, F16, 23) (dual of [1048614, 1048500, 24]-code) [i]Code Embedding in Larger Space
2Linear OA(16115, 1048615, F16, 23) (dual of [1048615, 1048500, 24]-code) [i]
3Linear OA(16116, 1048616, F16, 23) (dual of [1048616, 1048500, 24]-code) [i]
4Linear OOA(16113, 1048613, F16, 2, 23) (dual of [(1048613, 2), 2097113, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Digital (90, 113, 1048613)-net over F16 [i]
6Linear OA(16114, 1048615, F16, 23) (dual of [1048615, 1048501, 24]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OOA(16113, 524306, F16, 2, 23) (dual of [(524306, 2), 1048499, 24]-NRT-code) [i]OOA Folding
8Linear OOA(16113, 95328, F16, 23, 23) (dual of [(95328, 23), 2192431, 24]-NRT-code) [i]OOA Folding and Stacking with Additional Row