Information on Result #678243

Linear OA(4224, 1048639, F4, 29) (dual of [1048639, 1048415, 30]-code), using construction X applied to Ce(28) ⊂ Ce(21) based on
  1. linear OA(4211, 1048576, F4, 29) (dual of [1048576, 1048365, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
  2. 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]
  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(4225, 1048640, F4, 29) (dual of [1048640, 1048415, 30]-code) [i]Code Embedding in Larger Space
2Linear OA(4226, 1048641, F4, 29) (dual of [1048641, 1048415, 30]-code) [i]
3Linear OA(4223, 1048638, F4, 28) (dual of [1048638, 1048415, 29]-code) [i]Truncation
4Linear OOA(4224, 524319, F4, 2, 29) (dual of [(524319, 2), 1048414, 30]-NRT-code) [i]OOA Folding
5Linear OOA(4224, 349546, F4, 3, 29) (dual of [(349546, 3), 1048414, 30]-NRT-code) [i]
6Linear OOA(4224, 74902, F4, 29, 29) (dual of [(74902, 29), 2171934, 30]-NRT-code) [i]OOA Folding and Stacking with Additional Row