MinT - Information on Result #2798088

Information on Result #2798088

Linear OOA(3²¹⁵, 2391514, F₃, 4, 16) (dual of [(2391514, 4), 9565841, 17]-NRT-code), using 3¹ times duplication based on linear OOA(3²¹⁴, 2391514, F₃, 4, 16) (dual of [(2391514, 4), 9565842, 17]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁴, 22, F₃, 4, 8) (dual of [(22, 4), 74, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (6, 14, 22)-net over F₃, using
    - linear code embedding found in a computer search [i]
2. linear OOA(3²⁰⁰, 2391492, F₃, 4, 16) (dual of [(2391492, 4), 9565768, 17]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(3²⁰⁰, 4782984, F₃, 2, 16) (dual of [(4782984, 2), 9565768, 17]-NRT-code), using
    - trace code [i] based on linear OOA(9¹⁰⁰, 2391492, F₉, 2, 16) (dual of [(2391492, 2), 4782884, 17]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(9¹⁰⁰, 4782984, F₉, 16) (dual of [4782984, 4782884, 17]-code), using
        constructionÂ X applied to C_e(15) âŠ‚ C_e(13) [i] based on
        linear OA(9⁹⁹, 4782969, F₉, 16) (dual of [4782969, 4782870, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(9⁸⁵, 4782969, F₉, 14) (dual of [4782969, 4782884, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(9¹, 15, F₉, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 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, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.