Information on Result #734235

Linear OA(3245, 1071, F32, 18) (dual of [1071, 1026, 19]-code), using (u, u+v)-construction based on
  1. linear OA(3210, 44, F32, 9) (dual of [44, 34, 10]-code), using
  2. linear OA(3235, 1027, F32, 18) (dual of [1027, 992, 19]-code), using
    • construction XX applied to C1 = C([1022,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([1022,16]) [i] based on
      1. linear OA(3233, 1023, F32, 17) (dual of [1023, 990, 18]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [i]
      2. linear OA(3233, 1023, F32, 17) (dual of [1023, 990, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
      3. linear OA(3235, 1023, F32, 18) (dual of [1023, 988, 19]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
      4. linear OA(3231, 1023, F32, 16) (dual of [1023, 992, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
      5. linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(320, 2, F32, 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(3245, 535, F32, 2, 18) (dual of [(535, 2), 1025, 19]-NRT-code) [i]OOA Folding