MinT - Information on Result #663818

Information on Result #663818

Linear OA(8¹⁴⁹, 2097179, F₈, 22) (dual of [2097179, 2097030, 23]-code), using (u,Â u+v)-construction based on

linear OA(8¹⁵, 27, F₈, 11) (dual of [27, 12, 12]-code), using
- constructionÂ X applied to AG(F,6P) âŠ‚ AG(F,7P) [i] based on
  1. linear OA(8¹⁴, 24, F₈, 11) (dual of [24, 10, 12]-code), using algebraic-geometric code AG(F,6P) with degPÂ =Â 2 [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using the Klein quartic over F₈ [i]
  2. linear OA(8¹², 24, F₈, 9) (dual of [24, 12, 10]-code), using algebraic-geometric code AG(F,7P) with degPÂ =Â 2 [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24 (see above)
  3. linear OA(8¹, 3, F₈, 1) (dual of [3, 2, 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]
linear OA(8¹³⁴, 2097152, F₈, 22) (dual of [2097152, 2097018, 23]-code), using
- an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Mode: Constructive and linear.

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