Information on Result #734511

Linear OA(4953, 2647, F49, 19) (dual of [2647, 2594, 20]-code), using (u, u+v)-construction based on
  1. linear OA(4916, 244, F49, 9) (dual of [244, 228, 10]-code), using
    • construction XX applied to C1 = C([239,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([239,7]) [i] based on
      1. 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]
      2. linear OA(4914, 240, F49, 8) (dual of [240, 226, 9]-code), using the expurgated narrow-sense BCH-code C(I) with length 240 | 492−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(4916, 240, F49, 9) (dual of [240, 224, 10]-code), using the BCH-code C(I) with length 240 | 492−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
      4. 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]
      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(4937, 2403, F49, 19) (dual of [2403, 2366, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(17) [i] based on
      1. linear OA(4937, 2401, F49, 19) (dual of [2401, 2364, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(4935, 2401, F49, 18) (dual of [2401, 2366, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(4953, 1323, F49, 2, 19) (dual of [(1323, 2), 2593, 20]-NRT-code) [i]OOA Folding
2Linear OOA(4953, 882, F49, 3, 19) (dual of [(882, 3), 2593, 20]-NRT-code) [i]