Information on Result #712254

Linear OA(5147, 675, F5, 42) (dual of [675, 528, 43]-code), using construction XX applied to C1 = C([618,30]), C2 = C([0,35]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([618,35]) 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 = {−6,−5,…,30}, and designed minimum distance d ≥ |I|+1 = 38 [i]
  2. linear OA(5111, 624, F5, 36) (dual of [624, 513, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
  3. linear OA(5131, 624, F5, 42) (dual of [624, 493, 43]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−6,−5,…,35}, and designed minimum distance d ≥ |I|+1 = 43 [i]
  4. linear OA(595, 624, F5, 31) (dual of [624, 529, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
  5. linear OA(59, 28, F5, 5) (dual of [28, 19, 6]-code), using
    • construction XX applied to C1 = C({0,1,2,19}), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,3,19}) [i] based on
      1. linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,19}, and minimum distance d ≥ |{−1,0,1,2}|+1 = 5 (BCH-bound) [i]
      2. linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
      3. linear OA(59, 24, F5, 5) (dual of [24, 15, 6]-code), using the primitive cyclic code C(A) with length 24 = 52−1, defining set A = {0,1,2,3,19}, and minimum distance d ≥ |{−1,0,1,2,3}|+1 = 6 (BCH-bound) [i]
      4. linear OA(55, 24, F5, 3) (dual of [24, 19, 4]-code or 24-cap in PG(4,5)), using the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
      5. linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code) (see above)
  6. linear OA(57, 23, F5, 4) (dual of [23, 16, 5]-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(5147, 337, F5, 2, 42) (dual of [(337, 2), 527, 43]-NRT-code) [i]OOA Folding
2Linear OOA(5147, 225, F5, 3, 42) (dual of [(225, 3), 528, 43]-NRT-code) [i]