Information on Result #678187

Linear OA(4246, 1048611, F4, 33) (dual of [1048611, 1048365, 34]-code), using construction X applied to Ce(32) ⊂ Ce(28) based on
  1. linear OA(4241, 1048576, F4, 33) (dual of [1048576, 1048335, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
  2. 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]
  3. linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), 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(4246, 1048611, F4, 32) (dual of [1048611, 1048365, 33]-code) [i]Strength Reduction
2Linear OA(4247, 1048612, F4, 33) (dual of [1048612, 1048365, 34]-code) [i]Code Embedding in Larger Space
3Linear OA(4248, 1048613, F4, 33) (dual of [1048613, 1048365, 34]-code) [i]
4Linear OA(4249, 1048614, F4, 33) (dual of [1048614, 1048365, 34]-code) [i]
5Linear OA(4250, 1048615, F4, 33) (dual of [1048615, 1048365, 34]-code) [i]
6Linear OA(4245, 1048610, F4, 32) (dual of [1048610, 1048365, 33]-code) [i]Truncation
7Linear OOA(4246, 524305, F4, 2, 33) (dual of [(524305, 2), 1048364, 34]-NRT-code) [i]OOA Folding
8Linear OOA(4246, 349537, F4, 3, 33) (dual of [(349537, 3), 1048365, 34]-NRT-code) [i]
9Linear OOA(4246, 65538, F4, 33, 33) (dual of [(65538, 33), 2162508, 34]-NRT-code) [i]OOA Folding and Stacking with Additional Row