Information on Result #707660

Linear OA(467, 1049, F4, 17) (dual of [1049, 982, 18]-code), using construction XX applied to C1 = C([1019,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1019,12]) based on
  1. linear OA(456, 1023, F4, 15) (dual of [1023, 967, 16]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,10}, and designed minimum distance d ≥ |I|+1 = 16 [i]
  2. linear OA(446, 1023, F4, 13) (dual of [1023, 977, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
  3. linear OA(461, 1023, F4, 17) (dual of [1023, 962, 18]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,12}, and designed minimum distance d ≥ |I|+1 = 18 [i]
  4. linear OA(441, 1023, F4, 11) (dual of [1023, 982, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
  5. linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), using
  6. linear OA(41, 6, F4, 1) (dual of [6, 5, 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 OOA(467, 943, F4, 2, 17) (dual of [(943, 2), 1819, 18]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(467, 943, F4, 3, 17) (dual of [(943, 3), 2762, 18]-NRT-code) [i]
3Digital (50, 67, 943)-net over F4 [i]
4Linear OOA(467, 524, F4, 2, 17) (dual of [(524, 2), 981, 18]-NRT-code) [i]OOA Folding
5Linear OOA(467, 349, F4, 3, 17) (dual of [(349, 3), 980, 18]-NRT-code) [i]