Information on Result #734533

Linear OA(4947, 2647, F49, 17) (dual of [2647, 2600, 18]-code), using (u, u+v)-construction based on
  1. linear OA(4914, 244, F49, 8) (dual of [244, 230, 9]-code), using
    • construction XX applied to C1 = C([239,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([239,6]) [i] based on
      1. linear OA(4912, 240, F49, 7) (dual of [240, 228, 8]-code), using the BCH-code C(I) with length 240 | 492−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
      2. linear OA(4912, 240, F49, 7) (dual of [240, 228, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 240 | 492−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(4914, 240, F49, 8) (dual of [240, 226, 9]-code), using the BCH-code C(I) with length 240 | 492−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
      4. linear OA(4910, 240, F49, 6) (dual of [240, 230, 7]-code), using the expurgated narrow-sense BCH-code C(I) with length 240 | 492−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
      5. linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code) (see above)
  2. linear OA(4933, 2403, F49, 17) (dual of [2403, 2370, 18]-code), using
    • construction X applied to Ce(16) ⊂ Ce(15) [i] based on
      1. linear OA(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      2. linear OA(4931, 2401, F49, 16) (dual of [2401, 2370, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
      3. linear OA(490, 2, F49, 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(4947, 1323, F49, 2, 17) (dual of [(1323, 2), 2599, 18]-NRT-code) [i]OOA Folding
2Linear OOA(4947, 882, F49, 3, 17) (dual of [(882, 3), 2599, 18]-NRT-code) [i]