Information on Result #682398

Linear OA(5146, 78159, F5, 25) (dual of [78159, 78013, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,10]) based on
  1. linear OA(5141, 78126, F5, 25) (dual of [78126, 77985, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
  2. linear OA(5113, 78126, F5, 21) (dual of [78126, 78013, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  3. linear OA(55, 33, F5, 3) (dual of [33, 28, 4]-code or 33-cap in PG(4,5)), using

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 OA(5147, 78160, F5, 25) (dual of [78160, 78013, 26]-code) [i]Code Embedding in Larger Space
2Linear OA(5148, 78161, F5, 25) (dual of [78161, 78013, 26]-code) [i]
3Linear OA(5149, 78162, F5, 25) (dual of [78162, 78013, 26]-code) [i]
4Linear OOA(5146, 60094, F5, 2, 25) (dual of [(60094, 2), 120042, 26]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(5146, 60094, F5, 3, 25) (dual of [(60094, 3), 180136, 26]-NRT-code) [i]
6Digital (121, 146, 60094)-net over F5 [i]
7Linear OA(5148, 78162, F5, 25) (dual of [78162, 78014, 26]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OA(5149, 78164, F5, 25) (dual of [78164, 78015, 26]-code) [i]
9Linear OOA(5146, 39079, F5, 2, 25) (dual of [(39079, 2), 78012, 26]-NRT-code) [i]OOA Folding
10Linear OOA(5146, 26053, F5, 3, 25) (dual of [(26053, 3), 78013, 26]-NRT-code) [i]
11Linear OOA(5146, 6513, F5, 25, 25) (dual of [(6513, 25), 162679, 26]-NRT-code) [i]OOA Folding and Stacking with Additional Row