Information on Result #711376

Linear OA(575, 638, F5, 23) (dual of [638, 563, 24]-code), using construction XX applied to C1 = C([622,18]), C2 = C([0,20]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([622,20]) based on
  1. linear OA(569, 624, F5, 21) (dual of [624, 555, 22]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
  2. linear OA(565, 624, F5, 21) (dual of [624, 559, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
  3. linear OA(573, 624, F5, 23) (dual of [624, 551, 24]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,20}, and designed minimum distance d ≥ |I|+1 = 24 [i]
  4. linear OA(561, 624, F5, 19) (dual of [624, 563, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(575, 616, F5, 2, 23) (dual of [(616, 2), 1157, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(575, 616, F5, 3, 23) (dual of [(616, 3), 1773, 24]-NRT-code) [i]
3Digital (52, 75, 616)-net over F5 [i]
4Linear OA(576, 640, F5, 23) (dual of [640, 564, 24]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OOA(575, 319, F5, 2, 23) (dual of [(319, 2), 563, 24]-NRT-code) [i]OOA Folding
6Linear OOA(575, 212, F5, 3, 23) (dual of [(212, 3), 561, 24]-NRT-code) [i]