MinT - Information on Result #1014799

Information on Result #1014799

Linear OOA(8¹⁰⁰, 10950, F₈, 3, 20) (dual of [(10950, 3), 32750, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹³, 24, F₈, 3, 10) (dual of [(24, 3), 59, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,61P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8⁸⁷, 10926, F₈, 3, 20) (dual of [(10926, 3), 32691, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8⁸⁷, 32778, F₈, 20) (dual of [32778, 32691, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁸⁷, 32779, F₈, 20) (dual of [32779, 32692, 21]-code), using
    - constructionÂ X applied to C_e(19) âŠ‚ C_e(17) [i] based on
      1. linear OA(8⁸⁶, 32768, F₈, 20) (dual of [32768, 32682, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      2. linear OA(8⁷⁶, 32768, F₈, 18) (dual of [32768, 32692, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      3. linear OA(8¹, 11, F₈, 1) (dual of [11, 10, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 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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