Information on Result #710950

Linear OA(543, 638, F5, 13) (dual of [638, 595, 14]-code), using construction XX applied to C1 = C([622,8]), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([622,10]) based on
  1. linear OA(537, 624, F5, 11) (dual of [624, 587, 12]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
  2. linear OA(533, 624, F5, 11) (dual of [624, 591, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(541, 624, F5, 13) (dual of [624, 583, 14]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [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(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(543, 565, F5, 2, 13) (dual of [(565, 2), 1087, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(543, 565, F5, 3, 13) (dual of [(565, 3), 1652, 14]-NRT-code) [i]
3Digital (30, 43, 565)-net over F5 [i]
4Linear OA(544, 640, F5, 13) (dual of [640, 596, 14]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OOA(543, 319, F5, 2, 13) (dual of [(319, 2), 595, 14]-NRT-code) [i]OOA Folding
6Linear OOA(543, 212, F5, 3, 13) (dual of [(212, 3), 593, 14]-NRT-code) [i]