Information on Result #679677

Linear OA(4222, 4119, F4, 49) (dual of [4119, 3897, 50]-code), using construction X applied to Ce(48) ⊂ Ce(44) based on
  1. linear OA(4217, 4096, F4, 49) (dual of [4096, 3879, 50]-code), using an extension Ce(48) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
  2. linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
  3. linear OA(45, 23, F4, 3) (dual of [23, 18, 4]-code or 23-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(4222, 4119, F4, 48) (dual of [4119, 3897, 49]-code) [i]Strength Reduction
2Linear OA(4223, 4120, F4, 49) (dual of [4120, 3897, 50]-code) [i]Code Embedding in Larger Space
3Linear OA(4221, 4118, F4, 48) (dual of [4118, 3897, 49]-code) [i]Truncation
4Linear OOA(4222, 4112, F4, 2, 49) (dual of [(4112, 2), 8002, 50]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(4222, 4112, F4, 3, 49) (dual of [(4112, 3), 12114, 50]-NRT-code) [i]
6Digital (173, 222, 4112)-net over F4 [i]
7Linear OA(4223, 4121, F4, 49) (dual of [4121, 3898, 50]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OA(4224, 4123, F4, 49) (dual of [4123, 3899, 50]-code) [i]
9Linear OOA(4222, 2059, F4, 2, 49) (dual of [(2059, 2), 3896, 50]-NRT-code) [i]OOA Folding
10Linear OOA(4222, 1373, F4, 3, 49) (dual of [(1373, 3), 3897, 50]-NRT-code) [i]