Information on Result #679991

Linear OA(4106, 4130, F4, 22) (dual of [4130, 4024, 23]-code), using construction XX applied to Ce(21) ⊂ Ce(16) ⊂ Ce(14) based on
  1. linear OA(497, 4096, F4, 22) (dual of [4096, 3999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  2. linear OA(473, 4096, F4, 17) (dual of [4096, 4023, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(467, 4096, F4, 15) (dual of [4096, 4029, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  4. linear OA(47, 32, F4, 4) (dual of [32, 25, 5]-code), 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(4107, 4131, F4, 22) (dual of [4131, 4024, 23]-code) [i]Code Embedding in Larger Space
2Linear OA(4108, 4132, F4, 22) (dual of [4132, 4024, 23]-code) [i]
3Linear OA(4109, 4133, F4, 22) (dual of [4133, 4024, 23]-code) [i]
4Linear OOA(4106, 3993, F4, 2, 22) (dual of [(3993, 2), 7880, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(4106, 3993, F4, 3, 22) (dual of [(3993, 3), 11873, 23]-NRT-code) [i]
6Digital (84, 106, 3993)-net over F4 [i]
7Linear OOA(4106, 2065, F4, 2, 22) (dual of [(2065, 2), 4024, 23]-NRT-code) [i]OOA Folding