Information on Result #711026

Linear OA(568, 663, F5, 18) (dual of [663, 595, 19]-code), using construction XX applied to C1 = C([619,8]), C2 = C([0,12]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([619,12]) based on
  1. linear OA(545, 624, F5, 14) (dual of [624, 579, 15]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−5,−4,…,8}, and designed minimum distance d ≥ |I|+1 = 15 [i]
  2. linear OA(541, 624, F5, 13) (dual of [624, 583, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
  3. linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−5,−4,…,12}, and designed minimum distance d ≥ |I|+1 = 19 [i]
  4. linear OA(529, 624, F5, 9) (dual of [624, 595, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
  5. linear OA(57, 23, F5, 4) (dual of [23, 16, 5]-code), using
  6. linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), 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(568, 331, F5, 2, 18) (dual of [(331, 2), 594, 19]-NRT-code) [i]OOA Folding
2Linear OOA(568, 221, F5, 3, 18) (dual of [(221, 3), 595, 19]-NRT-code) [i]