Information on Result #679984

Linear OA(4116, 4122, F4, 25) (dual of [4122, 4006, 26]-code), using construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(18) based on
  1. linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  2. linear OA(491, 4096, F4, 21) (dual of [4096, 4005, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  3. linear OA(485, 4096, F4, 19) (dual of [4096, 4011, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(4115, 4121, F4, 24) (dual of [4121, 4006, 25]-code) [i]Truncation
2Linear OOA(4116, 3200, F4, 2, 25) (dual of [(3200, 2), 6284, 26]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(4116, 3200, F4, 3, 25) (dual of [(3200, 3), 9484, 26]-NRT-code) [i]
4Digital (91, 116, 3200)-net over F4 [i]
5Linear OOA(4116, 2061, F4, 2, 25) (dual of [(2061, 2), 4006, 26]-NRT-code) [i]OOA Folding
6Linear OOA(4116, 1374, F4, 3, 25) (dual of [(1374, 3), 4006, 26]-NRT-code) [i]