Information on Result #709771

Linear OA(519, 130, F5, 8) (dual of [130, 111, 9]-code), using construction XX applied to C1 = C([123,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([123,6]) based on
  1. linear OA(516, 124, F5, 7) (dual of [124, 108, 8]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
  2. linear OA(516, 124, F5, 7) (dual of [124, 108, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
  3. linear OA(519, 124, F5, 8) (dual of [124, 105, 9]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
  4. linear OA(513, 124, F5, 6) (dual of [124, 111, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
  5. linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-code), using
  6. linear OA(50, 3, F5, 0) (dual of [3, 3, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(521, 136, F5, 8) (dual of [136, 115, 9]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(522, 149, F5, 8) (dual of [149, 127, 9]-code) [i]
3Linear OA(523, 176, F5, 8) (dual of [176, 153, 9]-code) [i]
4Linear OOA(519, 65, F5, 2, 8) (dual of [(65, 2), 111, 9]-NRT-code) [i]OOA Folding
5Linear OOA(519, 43, F5, 3, 8) (dual of [(43, 3), 110, 9]-NRT-code) [i]