MinT - Information on Result #1015273

Information on Result #1015273

Linear OOA(8¹⁷², 10950, F₈, 3, 35) (dual of [(10950, 3), 32678, 36]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8²⁰, 24, F₈, 3, 17) (dual of [(24, 3), 52, 18]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,54P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8¹⁵², 10926, F₈, 3, 35) (dual of [(10926, 3), 32626, 36]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹⁵², 32778, F₈, 35) (dual of [32778, 32626, 36]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹⁵², 32780, F₈, 35) (dual of [32780, 32628, 36]-code), using
    - constructionÂ X applied to C([0,17]) âŠ‚ C([0,16]) [i] based on
      1. linear OA(8¹⁵¹, 32769, F₈, 35) (dual of [32769, 32618, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 8¹⁰âˆ’1, defining interval IÂ =Â [0,17], and minimum distance dÂ â‰¥ |{−17,−16,…,17}|+1Â =Â 36 (BCH-bound) [i]
      2. linear OA(8¹⁴¹, 32769, F₈, 33) (dual of [32769, 32628, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 8¹⁰âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [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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