Information on Result #678780

Linear OA(4169, 65600, F4, 26) (dual of [65600, 65431, 27]-code), using construction X applied to Ce(25) ⊂ Ce(17) based on
  1. linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(4105, 65536, F4, 18) (dual of [65536, 65431, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(4170, 65601, F4, 26) (dual of [65601, 65431, 27]-code) [i]Code Embedding in Larger Space
2Linear OA(4171, 65602, F4, 26) (dual of [65602, 65431, 27]-code) [i]
3Linear OA(4171, 65603, F4, 26) (dual of [65603, 65432, 27]-code) [i]Construction X with VarÅ¡amov Bound
4Linear OOA(4169, 32800, F4, 2, 26) (dual of [(32800, 2), 65431, 27]-NRT-code) [i]OOA Folding
5Linear OOA(4169, 21866, F4, 3, 26) (dual of [(21866, 3), 65429, 27]-NRT-code) [i]
6Linear OOA(4169, 5046, F4, 26, 26) (dual of [(5046, 26), 131027, 27]-NRT-code) [i]OA Folding and Stacking