Information on Result #896219

Linear OOA(5146, 4194617, F5, 2, 16) (dual of [(4194617, 2), 8389088, 17]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(525, 316, F5, 2, 8) (dual of [(316, 2), 607, 9]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(525, 632, F5, 8) (dual of [632, 607, 9]-code), using
      • construction XX applied to C1 = C([623,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([623,6]) [i] based on
        1. linear OA(521, 624, F5, 7) (dual of [624, 603, 8]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
        2. linear OA(521, 624, F5, 7) (dual of [624, 603, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
        3. linear OA(525, 624, F5, 8) (dual of [624, 599, 9]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
        4. linear OA(517, 624, F5, 6) (dual of [624, 607, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
        5. linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
        6. linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code) (see above)
  2. linear OOA(5121, 4194301, F5, 2, 16) (dual of [(4194301, 2), 8388481, 17]-NRT-code), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(5146, 1048654, F5, 18, 16) (dual of [(1048654, 18), 18875626, 17]-NRT-code) [i]OOA Folding and Stacking with Additional Row