Information on Result #678199

Linear OA(4156, 1048611, F4, 21) (dual of [1048611, 1048455, 22]-code), using construction X applied to Ce(20) ⊂ Ce(16) based on
  1. linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  2. linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(4156, 1048611, F4, 20) (dual of [1048611, 1048455, 21]-code) [i]Strength Reduction
2Linear OA(4157, 1048612, F4, 21) (dual of [1048612, 1048455, 22]-code) [i]Code Embedding in Larger Space
3Linear OA(4158, 1048613, F4, 21) (dual of [1048613, 1048455, 22]-code) [i]
4Linear OA(4159, 1048614, F4, 21) (dual of [1048614, 1048455, 22]-code) [i]
5Linear OA(4160, 1048615, F4, 21) (dual of [1048615, 1048455, 22]-code) [i]
6Linear OA(4155, 1048610, F4, 20) (dual of [1048610, 1048455, 21]-code) [i]Truncation
7Linear OA(4160, 1048616, F4, 21) (dual of [1048616, 1048456, 22]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OOA(4156, 524305, F4, 2, 21) (dual of [(524305, 2), 1048454, 22]-NRT-code) [i]OOA Folding
9Linear OOA(4156, 349537, F4, 3, 21) (dual of [(349537, 3), 1048455, 22]-NRT-code) [i]
10Linear OOA(4156, 104861, F4, 21, 21) (dual of [(104861, 21), 2201925, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row