MinT - Information on Result #1299922

Information on Result #1299922

Linear OA(4⁷⁹, 100, F₄, 42) (dual of [100, 21, 43]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4⁷⁸, 98, F₄, 42) (dual of [98, 20, 43]-code), using
- 1 times truncation [i] based on linear OA(4⁷⁹, 99, F₄, 43) (dual of [99, 20, 44]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(16²³, 33, F₁₆, 21) (dual of [33, 10, 22]-code), using
      - extended algebraic-geometric code AG_e(F,11P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
        a function field by SÃ©mirat [i]
    2. linear OA(4¹, 3, F₄, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OA(4⁷⁸, 99, F₄, 41) (dual of [99, 21, 42]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4⁷⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 76946 232981 783215 497152 946509 756045 574598 401288 [i]
linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 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: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(4⁸⁰, 102, F₄, 42) (dual of [102, 22, 43]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound