Information on Result #678251

Linear OA(4164, 1048639, F4, 21) (dual of [1048639, 1048475, 22]-code), using construction X applied to Ce(20) ⊂ Ce(13) based on
  1. linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  2. linear OA(4101, 1048576, F4, 14) (dual of [1048576, 1048475, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
  3. linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
    • the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]

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(4165, 1048640, F4, 21) (dual of [1048640, 1048475, 22]-code) [i]Code Embedding in Larger Space
2Linear OA(4163, 1048638, F4, 20) (dual of [1048638, 1048475, 21]-code) [i]Truncation
3Linear OOA(4164, 524319, F4, 2, 21) (dual of [(524319, 2), 1048474, 22]-NRT-code) [i]OOA Folding
4Linear OOA(4164, 349546, F4, 3, 21) (dual of [(349546, 3), 1048474, 22]-NRT-code) [i]
5Linear OOA(4164, 104863, F4, 21, 21) (dual of [(104863, 21), 2201959, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row