MinT - Information on Result #1298263

Information on Result #1298263

Linear OA(3⁹⁴, 119, F₃, 43) (dual of [119, 25, 44]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3⁹³, 117, F₃, 43) (dual of [117, 24, 44]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(3⁸⁹, 111, F₃, 43) (dual of [111, 22, 44]-code), using
    - 1 times truncation [i] based on linear OA(3⁹⁰, 112, F₃, 44) (dual of [112, 22, 45]-code), using
      - concatenation of two codes [i] based on
        linear OA(9¹⁷, 28, F₉, 14) (dual of [28, 11, 15]-code), using
        extended algebraic-geometric code AG_e(F,13P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
        the Hermitian function field over F₉ [i]
        linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
        extended Reedâ€“Solomon code RS_e(2,3) [i]
        Hamming code H(2,3) [i]
        Simplex code S(2,3) [i]
        the Tetracode [i]
  2. linear OA(3⁸⁹, 113, F₃, 40) (dual of [113, 24, 41]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3⁸⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 1 608826 119753 002912 866980 037122 777137 394369 [i]
  3. linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)) (see above)
linear OA(3⁹³, 118, F₃, 42) (dual of [118, 25, 43]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3⁹³Â > V_b^sâˆ’1(kâˆ’1)Â = 187 752165 971613 155137 532376 204853 619545 386291 [i]
linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3⁹⁵, 121, F₃, 43) (dual of [121, 26, 44]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound