MinT - Information on Result #1016425

Information on Result #1016425

Linear OOA(9¹⁴¹, 1594356, F₉, 3, 21) (dual of [(1594356, 3), 4782927, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹³, 28, F₉, 3, 10) (dual of [(28, 3), 71, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,73P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
  - the Hermitian function field over F₉ [i]
linear OOA(9¹²⁸, 1594328, F₉, 3, 21) (dual of [(1594328, 3), 4782856, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9¹²⁸, 4782984, F₉, 21) (dual of [4782984, 4782856, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(9¹²⁸, 4782985, F₉, 21) (dual of [4782985, 4782857, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(9¹²⁷, 4782970, F₉, 21) (dual of [4782970, 4782843, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 9¹⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(9¹¹³, 4782970, F₉, 19) (dual of [4782970, 4782857, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 9¹⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(9¹, 15, F₉, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(9¹, s, F₉, 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.