Information on Result #711160

Linear OA(559, 638, F5, 18) (dual of [638, 579, 19]-code), using construction XX applied to C1 = C([622,13]), C2 = C([0,15]), C3 = C1 + C2 = C([0,13]), and C∩ = C1 ∩ C2 = C([622,15]) based on
  1. linear OA(553, 624, F5, 16) (dual of [624, 571, 17]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,13}, and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. linear OA(549, 624, F5, 16) (dual of [624, 575, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [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 = {−2,−1,…,15}, and designed minimum distance d ≥ |I|+1 = 19 [i]
  4. linear OA(545, 624, F5, 14) (dual of [624, 579, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
  5. linear OA(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
  6. linear OA(51, 5, F5, 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 OOA(559, 571, F5, 2, 18) (dual of [(571, 2), 1083, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(559, 571, F5, 3, 18) (dual of [(571, 3), 1654, 19]-NRT-code) [i]
3Digital (41, 59, 571)-net over F5 [i]
4Linear OA(560, 640, F5, 18) (dual of [640, 580, 19]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OOA(559, 319, F5, 2, 18) (dual of [(319, 2), 579, 19]-NRT-code) [i]OOA Folding
6Linear OOA(559, 212, F5, 3, 18) (dual of [(212, 3), 577, 19]-NRT-code) [i]