Information on Result #682490

Linear OA(553, 78149, F5, 9) (dual of [78149, 78096, 10]-code), using construction X applied to Ce(8) ⊂ Ce(5) based on
  1. linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  2. linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
  3. linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
    • the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]

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(554, 78150, F5, 9) (dual of [78150, 78096, 10]-code) [i]Code Embedding in Larger Space
2Linear OOA(553, 78149, F5, 2, 9) (dual of [(78149, 2), 156245, 10]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(553, 78149, F5, 3, 9) (dual of [(78149, 3), 234394, 10]-NRT-code) [i]
4Digital (44, 53, 78149)-net over F5 [i]
5Linear OA(554, 78151, F5, 9) (dual of [78151, 78097, 10]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OA(555, 78153, F5, 9) (dual of [78153, 78098, 10]-code) [i]
7Linear OOA(553, 39074, F5, 2, 9) (dual of [(39074, 2), 78095, 10]-NRT-code) [i]OOA Folding
8Linear OOA(553, 26049, F5, 3, 9) (dual of [(26049, 3), 78094, 10]-NRT-code) [i]
9Linear OOA(553, 19537, F5, 9, 9) (dual of [(19537, 9), 175780, 10]-NRT-code) [i]OOA Folding and Stacking with Additional Row