Information on Result #678253

Linear OA(4151, 1048636, F4, 19) (dual of [1048636, 1048485, 20]-code), using construction X applied to Ce(18) ⊂ Ce(12) based on
  1. linear OA(4141, 1048576, F4, 19) (dual of [1048576, 1048435, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(410, 60, F4, 5) (dual of [60, 50, 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(4152, 1048637, F4, 19) (dual of [1048637, 1048485, 20]-code) [i]Code Embedding in Larger Space
2Linear OA(4153, 1048638, F4, 19) (dual of [1048638, 1048485, 20]-code) [i]
3Linear OA(4154, 1048639, F4, 19) (dual of [1048639, 1048485, 20]-code) [i]
4Linear OA(4153, 1048639, F4, 19) (dual of [1048639, 1048486, 20]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OA(4154, 1048641, F4, 19) (dual of [1048641, 1048487, 20]-code) [i]
6Linear OOA(4151, 524318, F4, 2, 19) (dual of [(524318, 2), 1048485, 20]-NRT-code) [i]OOA Folding
7Linear OOA(4151, 349545, F4, 3, 19) (dual of [(349545, 3), 1048484, 20]-NRT-code) [i]
8Linear OOA(4151, 116515, F4, 19, 19) (dual of [(116515, 19), 2213634, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row