MinT - Information on Result #1549172

Information on Result #1549172

Linear OOA(5¹¹⁰, 908175, F₅, 3, 16) (dual of [(908175, 3), 2724415, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(5¹¹⁰, 908175, F₅, 2, 16) (dual of [(908175, 2), 1816240, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(5¹¹⁰, 976567, F₅, 2, 16) (dual of [(976567, 2), 1953024, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹¹⁰, 1953134, F₅, 16) (dual of [1953134, 1953024, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹¹⁰, 1953135, F₅, 16) (dual of [1953135, 1953025, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(13) [i] based on
      1. linear OA(5¹⁰⁹, 1953125, F₅, 16) (dual of [1953125, 1953016, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(5¹⁰⁰, 1953125, F₅, 14) (dual of [1953125, 1953025, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1953124Â = 5⁹âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(5¹, 10, F₅, 1) (dual of [10, 9, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

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:

	Result		This result only	Method
1	Linear OOA(5¹¹⁰, 302724, F₅, 21, 16) (dual of [(302724, 21), 6357094, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row