Information on Result #711255

Linear OA(566, 637, F5, 20) (dual of [637, 571, 21]-code), using construction XX applied to C1 = C([622,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([622,17]) based on
  1. linear OA(561, 624, F5, 19) (dual of [624, 563, 20]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
  2. linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. linear OA(565, 624, F5, 20) (dual of [624, 559, 21]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,17}, and designed minimum distance d ≥ |I|+1 = 21 [i]
  4. linear OA(553, 624, F5, 17) (dual of [624, 571, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
  5. linear OA(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
  6. linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-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 OA(567, 643, F5, 20) (dual of [643, 576, 21]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OOA(566, 318, F5, 2, 20) (dual of [(318, 2), 570, 21]-NRT-code) [i]OOA Folding
3Linear OOA(566, 212, F5, 3, 20) (dual of [(212, 3), 570, 21]-NRT-code) [i]