MinT - Information on Result #671180

Information on Result #671180

Linear OA(128⁶⁸, 16578, F₁₂₈, 26) (dual of [16578, 16510, 27]-code), using (u,Â u+v)-construction based on

linear OA(128¹⁷, 194, F₁₂₈, 13) (dual of [194, 177, 14]-code), using
- constructionÂ X applied to AG(F,177P) âŠ‚ AG(F,179P) [i] based on
  1. linear OA(128¹⁶, 191, F₁₂₈, 13) (dual of [191, 175, 14]-code), using algebraic-geometric code AG(F,177P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
    - a function field by SÃ©mirat [i]
  2. linear OA(128¹⁴, 191, F₁₂₈, 11) (dual of [191, 177, 12]-code), using algebraic-geometric code AG(F,179P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192 (see above)
  3. linear OA(128¹, 3, F₁₂₈, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(128⁵¹, 16384, F₁₂₈, 26) (dual of [16384, 16333, 27]-code), using
- an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

Mode: Constructive and linear.

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