MinT - Information on Result #1015052

Information on Result #1015052

Linear OOA(8¹⁶³, 87409, F₈, 3, 28) (dual of [(87409, 3), 262064, 29]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁷, 24, F₈, 3, 14) (dual of [(24, 3), 55, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,57P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8¹⁴⁶, 87385, F₈, 3, 28) (dual of [(87385, 3), 262009, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹⁴⁶, 262155, F₈, 28) (dual of [262155, 262009, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹⁴⁶, 262157, F₈, 28) (dual of [262157, 262011, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(25) [i] based on
      1. linear OA(8¹⁴⁵, 262144, F₈, 28) (dual of [262144, 261999, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(8¹³³, 262144, F₈, 26) (dual of [262144, 262011, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      3. linear OA(8¹, 13, F₈, 1) (dual of [13, 12, 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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