Information on Result #678732

Linear OA(4179, 65578, F4, 29) (dual of [65578, 65399, 30]-code), using construction X applied to Ce(28) ⊂ Ce(22) based on
  1. linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
  2. linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  3. linear OA(410, 42, F4, 5) (dual of [42, 32, 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(4180, 65579, F4, 29) (dual of [65579, 65399, 30]-code) [i]Code Embedding in Larger Space
2Linear OA(4181, 65580, F4, 29) (dual of [65580, 65399, 30]-code) [i]
3Linear OA(4178, 65577, F4, 28) (dual of [65577, 65399, 29]-code) [i]Truncation
4Linear OOA(4179, 33896, F4, 2, 29) (dual of [(33896, 2), 67613, 30]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(4179, 33896, F4, 3, 29) (dual of [(33896, 3), 101509, 30]-NRT-code) [i]
6Digital (150, 179, 33896)-net over F4 [i]
7Linear OOA(4179, 32789, F4, 2, 29) (dual of [(32789, 2), 65399, 30]-NRT-code) [i]OOA Folding
8Linear OOA(4179, 21859, F4, 3, 29) (dual of [(21859, 3), 65398, 30]-NRT-code) [i]
9Linear OOA(4179, 4684, F4, 29, 29) (dual of [(4684, 29), 135657, 30]-NRT-code) [i]OOA Folding and Stacking with Additional Row