Information on Result #709857

Linear OA(531, 130, F5, 13) (dual of [130, 99, 14]-code), using construction XX applied to C1 = C([123,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([123,11]) based on
  1. linear OA(528, 124, F5, 12) (dual of [124, 96, 13]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
  2. linear OA(528, 124, F5, 12) (dual of [124, 96, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(531, 124, F5, 13) (dual of [124, 93, 14]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
  4. linear OA(525, 124, F5, 11) (dual of [124, 99, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [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(534, 142, F5, 13) (dual of [142, 108, 14]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(535, 155, F5, 13) (dual of [155, 120, 14]-code) [i]
3Linear OA(536, 173, F5, 13) (dual of [173, 137, 14]-code) [i]
4Linear OA(537, 196, F5, 13) (dual of [196, 159, 14]-code) [i]
5Linear OOA(531, 65, F5, 2, 13) (dual of [(65, 2), 99, 14]-NRT-code) [i]OOA Folding
6Linear OOA(531, 43, F5, 3, 13) (dual of [(43, 3), 98, 14]-NRT-code) [i]