Information on Result #706149

Linear OA(461, 287, F4, 18) (dual of [287, 226, 19]-code), using construction XX applied to C1 = C([251,9]), C2 = C([0,13]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([251,13]) based on
  1. linear OA(441, 255, F4, 14) (dual of [255, 214, 15]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,9}, and designed minimum distance d ≥ |I|+1 = 15 [i]
  2. linear OA(441, 255, F4, 14) (dual of [255, 214, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
  3. linear OA(453, 255, F4, 18) (dual of [255, 202, 19]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−4,−3,…,13}, and designed minimum distance d ≥ |I|+1 = 19 [i]
  4. linear OA(429, 255, F4, 10) (dual of [255, 226, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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(44, 16, F4, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,4)) (see above)

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(462, 288, F4, 18) (dual of [288, 226, 19]-code) [i]Code Embedding in Larger Space
2Linear OOA(461, 143, F4, 2, 18) (dual of [(143, 2), 225, 19]-NRT-code) [i]OOA Folding