MinT - Information on Result #1321794

Information on Result #1321794

Linear OA(9¹¹², 130, F₉, 79) (dual of [130, 18, 80]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(9¹¹¹, 128, F₉, 79) (dual of [128, 17, 80]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(9¹⁰⁵, 120, F₉, 79) (dual of [120, 15, 80]-code), using
    - discarding factors / shortening the dual code based on linear OA(9¹⁰⁵, 121, F₉, 79) (dual of [121, 16, 80]-code), using
      - 2 times truncation [i] based on linear OA(9¹⁰⁷, 123, F₉, 81) (dual of [123, 16, 82]-code), using
        a code from Grasslâ€™s database [i]
  2. linear OA(9¹⁰⁵, 122, F₉, 74) (dual of [122, 17, 75]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9¹⁰⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 15075 664291 555105 120078 195033 616901 152436 279870 947014 937504 300664 619326 783012 364214 048623 583236 526793 [i]
  3. linear OA(9⁴, 6, F₉, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,9)), using
    - discarding factors / shortening the dual code based on linear OA(9⁴, 9, F₉, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,9)), using
      - Reedâ€“Solomon code RS(5,9) [i]
linear OA(9¹¹¹, 129, F₉, 78) (dual of [129, 18, 79]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9¹¹¹Â > V_b^sâˆ’1(kâˆ’1)Â = 7239 879779 528213 718370 062309 716056 709101 511749 084069 952072 773147 881329 987563 550368 896752 169732 355180 786689 [i]
linear OA(9⁰, 1, F₉, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]

Mode: 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.