Information on Result #732906

Linear OA(2535, 705, F25, 13) (dual of [705, 670, 14]-code), using (u, u+v)-construction based on
  1. linear OA(2510, 77, F25, 6) (dual of [77, 67, 7]-code), using
    • 1 times truncation [i] based on linear OA(2511, 78, F25, 7) (dual of [78, 67, 8]-code), using
      • the BCH-code C(I) with length 78 | 252−1, defining interval I = {1,18,35,…,25}, and designed minimum distance d ≥ |I|+1 = 8 [i]
  2. linear OA(2525, 628, F25, 13) (dual of [628, 603, 14]-code), using
    • construction XX applied to C1 = C([623,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([623,11]) [i] based on
      1. linear OA(2523, 624, F25, 12) (dual of [624, 601, 13]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      2. linear OA(2523, 624, F25, 12) (dual of [624, 601, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(2525, 624, F25, 13) (dual of [624, 599, 14]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
      4. linear OA(2521, 624, F25, 11) (dual of [624, 603, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [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(2535, 352, F25, 2, 13) (dual of [(352, 2), 669, 14]-NRT-code) [i]OOA Folding