Information on Result #712194

Linear OA(5140, 666, F5, 41) (dual of [666, 526, 42]-code), using construction XX applied to C1 = C([619,31]), C2 = C([1,35]), C3 = C1 + C2 = C([1,31]), and C∩ = C1 ∩ C2 = C([619,35]) based on
  1. linear OA(5115, 624, F5, 37) (dual of [624, 509, 38]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−5,−4,…,31}, and designed minimum distance d ≥ |I|+1 = 38 [i]
  2. linear OA(5110, 624, F5, 35) (dual of [624, 514, 36]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
  3. linear OA(5127, 624, F5, 41) (dual of [624, 497, 42]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−5,−4,…,35}, and designed minimum distance d ≥ |I|+1 = 42 [i]
  4. linear OA(598, 624, F5, 31) (dual of [624, 526, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
  5. linear OA(59, 26, F5, 5) (dual of [26, 17, 6]-code), using
    • the expurgated narrow-sense BCH-code C(I) with length 26 | 54−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
  6. linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), 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(5140, 333, F5, 2, 41) (dual of [(333, 2), 526, 42]-NRT-code) [i]OOA Folding
2Linear OOA(5140, 222, F5, 3, 41) (dual of [(222, 3), 526, 42]-NRT-code) [i]