Information on Result #732187

Linear OA(25107, 694, F25, 43) (dual of [694, 587, 44]-code), using (u, u+v)-construction based on
  1. linear OA(2525, 66, F25, 21) (dual of [66, 41, 22]-code), using
  2. linear OA(2582, 628, F25, 43) (dual of [628, 546, 44]-code), using
    • construction XX applied to C1 = C([623,40]), C2 = C([0,41]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([623,41]) [i] based on
      1. linear OA(2580, 624, F25, 42) (dual of [624, 544, 43]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,40}, and designed minimum distance d ≥ |I|+1 = 43 [i]
      2. linear OA(2580, 624, F25, 42) (dual of [624, 544, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
      3. linear OA(2582, 624, F25, 43) (dual of [624, 542, 44]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,41}, and designed minimum distance d ≥ |I|+1 = 44 [i]
      4. linear OA(2578, 624, F25, 41) (dual of [624, 546, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
      5. linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)

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(25107, 347, F25, 2, 43) (dual of [(347, 2), 587, 44]-NRT-code) [i]OOA Folding