Information on Result #706146

Linear OA(454, 276, F4, 17) (dual of [276, 222, 18]-code), using construction XX applied to C1 = C([251,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([251,12]) based on
  1. linear OA(445, 255, F4, 15) (dual of [255, 210, 16]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,10}, and designed minimum distance d ≥ |I|+1 = 16 [i]
  2. linear OA(437, 255, F4, 13) (dual of [255, 218, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
  3. linear OA(449, 255, F4, 17) (dual of [255, 206, 18]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,12}, and designed minimum distance d ≥ |I|+1 = 18 [i]
  4. linear OA(433, 255, F4, 11) (dual of [255, 222, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [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(455, 277, F4, 17) (dual of [277, 222, 18]-code) [i]Code Embedding in Larger Space
2Linear OOA(454, 276, F4, 2, 17) (dual of [(276, 2), 498, 18]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(454, 276, F4, 3, 17) (dual of [(276, 3), 774, 18]-NRT-code) [i]
4Digital (37, 54, 276)-net over F4 [i]
5Linear OA(455, 278, F4, 17) (dual of [278, 223, 18]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(454, 138, F4, 2, 17) (dual of [(138, 2), 222, 18]-NRT-code) [i]OOA Folding