Information on Result #1301760

Linear OA(5117, 1953172, F5, 15) (dual of [1953172, 1953055, 16]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5114, 1953167, F5, 15) (dual of [1953167, 1953053, 16]-code), using
    • construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
      1. linear OA(5109, 1953126, F5, 15) (dual of [1953126, 1953017, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
      2. linear OA(573, 1953126, F5, 11) (dual of [1953126, 1953053, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1953126 | 518−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
      3. linear OA(55, 41, F5, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,5)), using
  2. linear OA(5114, 1953169, F5, 13) (dual of [1953169, 1953055, 14]-code), using Gilbert–VarÅ¡amov bound and bm = 5114 > Vbs−1(k−1) = 107 955339 541219 466852 100040 116705 258609 163895 280716 929865 106896 802259 564993 [i]
  3. linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using

Mode: 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(5117, 1953172, F5, 2, 15) (dual of [(1953172, 2), 3906227, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5117, 1953172, F5, 3, 15) (dual of [(1953172, 3), 5859399, 16]-NRT-code) [i]
3Digital (102, 117, 1953172)-net over F5 [i]
4Linear OOA(5117, 976586, F5, 2, 15) (dual of [(976586, 2), 1953055, 16]-NRT-code) [i]OOA Folding