Information on Result #1301903

Linear OA(5142, 1953160, F5, 19) (dual of [1953160, 1953018, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5139, 1953155, F5, 19) (dual of [1953155, 1953016, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(15) [i] based on
      1. linear OA(5136, 1953125, F5, 19) (dual of [1953125, 1952989, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
      3. linear OA(53, 30, F5, 2) (dual of [30, 27, 3]-code), using
  2. linear OA(5139, 1953157, F5, 17) (dual of [1953157, 1953018, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 5139 > Vbs−1(k−1) = 9 206729 588822 714215 055439 815886 740477 631776 408147 205825 645329 392295 635552 572090 074448 463763 008625 [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(5142, 976580, F5, 2, 19) (dual of [(976580, 2), 1953018, 20]-NRT-code) [i]OOA Folding
2Linear OOA(5142, 651053, F5, 3, 19) (dual of [(651053, 3), 1953017, 20]-NRT-code) [i]