MinT - Information on Result #896823

Information on Result #896823

Linear OOA(8¹⁶⁶, 16431, F₈, 2, 32) (dual of [(16431, 2), 32696, 33]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8²⁵, 45, F₈, 2, 16) (dual of [(45, 2), 65, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,73P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
  - an explicitly constructive algebraic function field [i]
linear OOA(8¹⁴¹, 16386, F₈, 2, 32) (dual of [(16386, 2), 32631, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8¹⁴¹, 32772, F₈, 32) (dual of [32772, 32631, 33]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹⁴¹, 32773, F₈, 32) (dual of [32773, 32632, 33]-code), using
    - 1 times truncation [i] based on linear OA(8¹⁴², 32774, F₈, 33) (dual of [32774, 32632, 34]-code), using
      - constructionÂ X applied to C_e(32) âŠ‚ C_e(30) [i] based on
        linear OA(8¹⁴¹, 32768, F₈, 33) (dual of [32768, 32627, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
        linear OA(8¹³⁶, 32768, F₈, 31) (dual of [32768, 32632, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [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.