Information on Result #678830

Linear OA(4191, 65567, F4, 31) (dual of [65567, 65376, 32]-code), using construction XX applied to Ce(30) ⊂ Ce(26) ⊂ Ce(25) based on
  1. linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
  3. linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(40, 1, F4, 0) (dual of [1, 1, 1]-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 OOA(4191, 34217, F4, 2, 31) (dual of [(34217, 2), 68243, 32]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4191, 34217, F4, 3, 31) (dual of [(34217, 3), 102460, 32]-NRT-code) [i]
3Digital (160, 191, 34217)-net over F4 [i]
4Linear OOA(4191, 32783, F4, 2, 31) (dual of [(32783, 2), 65375, 32]-NRT-code) [i]OOA Folding
5Linear OOA(4191, 4371, F4, 31, 31) (dual of [(4371, 31), 135310, 32]-NRT-code) [i]OOA Folding and Stacking with Additional Row