Information on Result #678806

Linear OA(4248, 65568, F4, 41) (dual of [65568, 65320, 42]-code), using construction XX applied to Ce(40) ⊂ Ce(36) ⊂ Ce(34) based on
  1. linear OA(4241, 65536, F4, 41) (dual of [65536, 65295, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
  2. linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  3. linear OA(4209, 65536, F4, 35) (dual of [65536, 65327, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
  4. linear OA(45, 30, F4, 3) (dual of [30, 25, 4]-code or 30-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(4247, 65567, F4, 40) (dual of [65567, 65320, 41]-code) [i]Truncation
2Linear OOA(4248, 33338, F4, 2, 41) (dual of [(33338, 2), 66428, 42]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(4248, 33338, F4, 3, 41) (dual of [(33338, 3), 99766, 42]-NRT-code) [i]
4Digital (207, 248, 33338)-net over F4 [i]
5Linear OOA(4248, 32784, F4, 2, 41) (dual of [(32784, 2), 65320, 42]-NRT-code) [i]OOA Folding
6Linear OOA(4248, 21856, F4, 3, 41) (dual of [(21856, 3), 65320, 42]-NRT-code) [i]