MinT - Information on Result #898795

Information on Result #898795

Linear OOA(16¹¹⁰, 2116, F₁₆, 2, 31) (dual of [(2116, 2), 4122, 32]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16²¹, 65, F₁₆, 2, 15) (dual of [(65, 2), 109, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,114P) [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(16⁸⁹, 2051, F₁₆, 2, 31) (dual of [(2051, 2), 4013, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁸⁹, 4102, F₁₆, 31) (dual of [4102, 4013, 32]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁸⁹, 4103, F₁₆, 31) (dual of [4103, 4014, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
      1. linear OA(16⁸⁸, 4096, F₁₆, 31) (dual of [4096, 4008, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 16³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [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(16¹, 7, F₁₆, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

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