Information on Result #678428

Linear OA(4141, 262176, F4, 21) (dual of [262176, 262035, 22]-code), using construction X applied to Ce(20) ⊂ Ce(16) based on
  1. linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  2. linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-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(4141, 262176, F4, 20) (dual of [262176, 262035, 21]-code) [i]Strength Reduction
2Linear OA(4142, 262177, F4, 21) (dual of [262177, 262035, 22]-code) [i]Code Embedding in Larger Space
3Linear OA(4143, 262178, F4, 21) (dual of [262178, 262035, 22]-code) [i]
4Linear OA(4144, 262179, F4, 21) (dual of [262179, 262035, 22]-code) [i]
5Linear OA(4145, 262180, F4, 21) (dual of [262180, 262035, 22]-code) [i]
6Linear OA(4140, 262175, F4, 20) (dual of [262175, 262035, 21]-code) [i]Truncation
7Linear OA(4145, 262181, F4, 21) (dual of [262181, 262036, 22]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OOA(4141, 131088, F4, 2, 21) (dual of [(131088, 2), 262035, 22]-NRT-code) [i]OOA Folding
9Linear OOA(4141, 87392, F4, 3, 21) (dual of [(87392, 3), 262035, 22]-NRT-code) [i]
10Linear OOA(4141, 26217, F4, 21, 21) (dual of [(26217, 21), 550416, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row