Information on Result #678776

Linear OA(4201, 65600, F4, 31) (dual of [65600, 65399, 32]-code), using construction X applied to Ce(30) ⊂ Ce(22) based on
  1. linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(416, 64, F4, 7) (dual of [64, 48, 8]-code), using
    • an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], 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(4202, 65601, F4, 31) (dual of [65601, 65399, 32]-code) [i]Code Embedding in Larger Space
2Linear OA(4203, 65602, F4, 31) (dual of [65602, 65399, 32]-code) [i]
3Linear OOA(4201, 55202, F4, 2, 31) (dual of [(55202, 2), 110203, 32]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(4201, 55202, F4, 3, 31) (dual of [(55202, 3), 165405, 32]-NRT-code) [i]
5Digital (170, 201, 55202)-net over F4 [i]
6Linear OA(4203, 65603, F4, 31) (dual of [65603, 65400, 32]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OOA(4201, 32800, F4, 2, 31) (dual of [(32800, 2), 65399, 32]-NRT-code) [i]OOA Folding
8Linear OOA(4201, 21866, F4, 3, 31) (dual of [(21866, 3), 65397, 32]-NRT-code) [i]
9Linear OOA(4201, 4373, F4, 31, 31) (dual of [(4373, 31), 135362, 32]-NRT-code) [i]OOA Folding and Stacking with Additional Row