MinT - Information on Result #898851

Information on Result #898851

Linear OOA(16¹¹⁶, 2119, F₁₆, 2, 33) (dual of [(2119, 2), 4122, 34]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16²², 65, F₁₆, 2, 16) (dual of [(65, 2), 108, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,113P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
  - the Hermitian function field over F₁₆ [i]
linear OOA(16⁹⁴, 2054, F₁₆, 2, 33) (dual of [(2054, 2), 4014, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁹⁴, 4108, F₁₆, 33) (dual of [4108, 4014, 34]-code), using
  - constructionÂ X applied to C_e(32) âŠ‚ C_e(28) [i] based on
    1. linear OA(16⁹¹, 4096, F₁₆, 33) (dual of [4096, 4005, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
    2. linear OA(16⁸², 4096, F₁₆, 29) (dual of [4096, 4014, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(16³, 12, F₁₆, 3) (dual of [12, 9, 4]-code or 12-arc in PG(2,16) or 12-cap in PG(2,16)), using
      - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
        Reedâ€“Solomon code RS(13,16) [i]

Mode: Constructive and linear.

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