Information on Result #706073

Linear OA(442, 276, F4, 13) (dual of [276, 234, 14]-code), using construction XX applied to C1 = C([251,6]), C2 = C([0,8]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([251,8]) based on
  1. linear OA(433, 255, F4, 11) (dual of [255, 222, 12]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,6}, and designed minimum distance d ≥ |I|+1 = 12 [i]
  2. linear OA(425, 255, F4, 9) (dual of [255, 230, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
  3. linear OA(437, 255, F4, 13) (dual of [255, 218, 14]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,8}, and designed minimum distance d ≥ |I|+1 = 14 [i]
  4. linear OA(421, 255, F4, 7) (dual of [255, 234, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
  5. linear OA(44, 16, F4, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,4)), using
  6. linear OA(41, 5, F4, 1) (dual of [5, 4, 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(443, 277, F4, 13) (dual of [277, 234, 14]-code) [i]Code Embedding in Larger Space
2Linear OOA(442, 276, F4, 2, 13) (dual of [(276, 2), 510, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(442, 276, F4, 3, 13) (dual of [(276, 3), 786, 14]-NRT-code) [i]
4Digital (29, 42, 276)-net over F4 [i]
5Linear OA(443, 278, F4, 13) (dual of [278, 235, 14]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(442, 138, F4, 2, 13) (dual of [(138, 2), 234, 14]-NRT-code) [i]OOA Folding