MinT - Information on Result #1014609

Information on Result #1014609

Linear OOA(8⁸², 10948, F₈, 3, 16) (dual of [(10948, 3), 32762, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹¹, 24, F₈, 3, 8) (dual of [(24, 3), 61, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,63P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8⁷¹, 10924, F₈, 3, 16) (dual of [(10924, 3), 32701, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8⁷¹, 32772, F₈, 16) (dual of [32772, 32701, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁷¹, 32773, F₈, 16) (dual of [32773, 32702, 17]-code), using
    - 1 times truncation [i] based on linear OA(8⁷², 32774, F₈, 17) (dual of [32774, 32702, 18]-code), using
      - constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
        linear OA(8⁷¹, 32768, F₈, 17) (dual of [32768, 32697, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(8⁶⁶, 32768, F₈, 15) (dual of [32768, 32702, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(8¹, 6, F₈, 1) (dual of [6, 5, 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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.