Information on Result #678250

Linear OA(4174, 1048639, F4, 22) (dual of [1048639, 1048465, 23]-code), using construction X applied to Ce(21) ⊂ Ce(14) based on
  1. linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  2. linear OA(4111, 1048576, F4, 15) (dual of [1048576, 1048465, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(4175, 1048640, F4, 22) (dual of [1048640, 1048465, 23]-code) [i]Code Embedding in Larger Space
2Linear OA(4176, 1048641, F4, 22) (dual of [1048641, 1048465, 23]-code) [i]
3Linear OOA(4174, 524319, F4, 2, 22) (dual of [(524319, 2), 1048464, 23]-NRT-code) [i]OOA Folding
4Linear OOA(4174, 349546, F4, 3, 22) (dual of [(349546, 3), 1048464, 23]-NRT-code) [i]
5Linear OOA(4174, 95330, F4, 22, 22) (dual of [(95330, 22), 2097086, 23]-NRT-code) [i]OA Folding and Stacking