Information on Result #679936

Linear OA(4188, 4122, F4, 41) (dual of [4122, 3934, 42]-code), using construction XX applied to Ce(40) ⊂ Ce(36) ⊂ Ce(34) based on
  1. linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
  2. linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  3. linear OA(4157, 4096, F4, 35) (dual of [4096, 3939, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
  4. linear OA(45, 24, F4, 3) (dual of [24, 19, 4]-code or 24-cap in PG(4,4)), using
  5. linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-code), 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(4187, 4121, F4, 40) (dual of [4121, 3934, 41]-code) [i]Truncation
2Linear OOA(4188, 3924, F4, 2, 41) (dual of [(3924, 2), 7660, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(4188, 3924, F4, 3, 41) (dual of [(3924, 3), 11584, 42]-NRT-code) [i]
4Digital (147, 188, 3924)-net over F4 [i]
5Linear OOA(4188, 2061, F4, 2, 41) (dual of [(2061, 2), 3934, 42]-NRT-code) [i]OOA Folding
6Linear OOA(4188, 1374, F4, 3, 41) (dual of [(1374, 3), 3934, 42]-NRT-code) [i]