Information on Result #677974

Linear OA(4171, 4194342, F4, 21) (dual of [4194342, 4194171, 22]-code), using construction X applied to Ce(20) ⊂ Ce(16) based on
  1. linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  2. linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-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(4171, 4194342, F4, 20) (dual of [4194342, 4194171, 21]-code) [i]Strength Reduction
2Linear OA(4172, 4194343, F4, 21) (dual of [4194343, 4194171, 22]-code) [i]Code Embedding in Larger Space
3Linear OA(4173, 4194344, F4, 21) (dual of [4194344, 4194171, 22]-code) [i]
4Linear OA(4174, 4194345, F4, 21) (dual of [4194345, 4194171, 22]-code) [i]
5Linear OA(4175, 4194346, F4, 21) (dual of [4194346, 4194171, 22]-code) [i]
6Linear OA(4170, 4194341, F4, 20) (dual of [4194341, 4194171, 21]-code) [i]Truncation
7Linear OA(4175, 4194347, F4, 21) (dual of [4194347, 4194172, 22]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OOA(4171, 2097171, F4, 2, 21) (dual of [(2097171, 2), 4194171, 22]-NRT-code) [i]OOA Folding
9Linear OOA(4171, 1398114, F4, 3, 21) (dual of [(1398114, 3), 4194171, 22]-NRT-code) [i]
10Linear OOA(4171, 419434, F4, 21, 21) (dual of [(419434, 21), 8807943, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row