MinT - Information on Result #1014942

Information on Result #1014942

Linear OOA(8¹⁶⁴, 699079, F₈, 3, 24) (dual of [(699079, 3), 2097073, 25]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁵, 24, F₈, 3, 12) (dual of [(24, 3), 57, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,59P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8¹⁴⁹, 699055, F₈, 3, 24) (dual of [(699055, 3), 2097016, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹⁴⁹, 2097165, F₈, 24) (dual of [2097165, 2097016, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹⁴⁹, 2097167, F₈, 24) (dual of [2097167, 2097018, 25]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
      1. linear OA(8¹⁴⁸, 2097152, F₈, 25) (dual of [2097152, 2097004, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. 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]
      3. linear OA(8¹, 15, F₈, 1) (dual of [15, 14, 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.