MinT - Information on Result #1011805

Information on Result #1011805

Linear OOA(4⁷⁰, 87393, F₄, 3, 10) (dual of [(87393, 3), 262109, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁶, 9, F₄, 3, 5) (dual of [(9, 3), 21, 6]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,21P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
  - the Hermitian function field over F₄ [i]
linear OOA(4⁶⁴, 87384, F₄, 3, 10) (dual of [(87384, 3), 262088, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4⁶⁴, 262152, F₄, 10) (dual of [262152, 262088, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁶⁴, 262153, F₄, 10) (dual of [262153, 262089, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(8) [i] based on
      1. linear OA(4⁶⁴, 262144, F₄, 10) (dual of [262144, 262080, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(4⁵⁵, 262144, F₄, 9) (dual of [262144, 262089, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      3. linear OA(4⁰, 9, F₄, 0) (dual of [9, 9, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.