MinT - Information on Result #1081273

Information on Result #1081273

Linear OOA(3¹⁰⁹, 4930, F₃, 4, 17) (dual of [(4930, 4), 19611, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁹, 7, F₃, 4, 8) (dual of [(7, 4), 19, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,19P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁰⁰, 4923, F₃, 4, 17) (dual of [(4923, 4), 19592, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹⁰⁰, 19692, F₃, 17) (dual of [19692, 19592, 18]-code), using
  - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
    1. linear OA(3¹⁰⁰, 19683, F₃, 17) (dual of [19683, 19583, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(3⁹¹, 19683, F₃, 16) (dual of [19683, 19592, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(3⁰, 9, F₃, 0) (dual of [9, 9, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

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