MinT - Information on Result #1013288

Information on Result #1013288

Linear OOA(5¹¹⁹, 651069, F₅, 3, 15) (dual of [(651069, 3), 1953088, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁰, 25, F₅, 3, 7) (dual of [(25, 3), 65, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (3, 10, 25)-net over F₅, using
  - linear code embedding found in a computer search [i]
linear OOA(5¹⁰⁹, 651044, F₅, 3, 15) (dual of [(651044, 3), 1953023, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5¹⁰⁹, 1953132, F₅, 15) (dual of [1953132, 1953023, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁰⁹, 1953134, F₅, 15) (dual of [1953134, 1953025, 16]-code), using
    - 1 times truncation [i] 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
        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]
        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]
        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: 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

None.