Information on Result #711410

Linear OA(578, 637, F5, 24) (dual of [637, 559, 25]-code), using construction XX applied to C1 = C([622,20]), C2 = C([0,21]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([622,21]) based on
  1. 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]
  2. linear OA(569, 624, F5, 22) (dual of [624, 555, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
  3. linear OA(577, 624, F5, 24) (dual of [624, 547, 25]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−2,−1,…,21}, and designed minimum distance d ≥ |I|+1 = 25 [i]
  4. 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]
  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(579, 643, F5, 24) (dual of [643, 564, 25]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(580, 662, F5, 24) (dual of [662, 582, 25]-code) [i]
3Linear OA(581, 698, F5, 24) (dual of [698, 617, 25]-code) [i]
4Linear OA(582, 744, F5, 24) (dual of [744, 662, 25]-code) [i]
5Linear OOA(578, 318, F5, 2, 24) (dual of [(318, 2), 558, 25]-NRT-code) [i]OOA Folding
6Linear OOA(578, 212, F5, 3, 24) (dual of [(212, 3), 558, 25]-NRT-code) [i]