MinT - Information on Result #2295746

Information on Result #2295746

Linear OA(2²¹⁹, 272, F₂, 75) (dual of [272, 53, 76]-code), using adding a parity check bit based on linear OA(2²¹⁸, 271, F₂, 74) (dual of [271, 53, 75]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(2²¹¹, 263, F₂, 74) (dual of [263, 52, 75]-code), using
  - 1 times truncation [i] based on linear OA(2²¹², 264, F₂, 75) (dual of [264, 52, 76]-code), using
    - concatenation of two codes [i] based on
      1. linear OA(16²⁰, 33, F₁₆, 18) (dual of [33, 13, 19]-code), using
        extended algebraic-geometric code AG_e(F,14P) [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(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
        Reedâ€“Muller code RM(1,3) [i]
        caps in base bÂ =Â 2 [i]
2. linear OA(2²¹¹, 264, F₂, 67) (dual of [264, 53, 68]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2²¹¹Â > V_b^sâˆ’1(kâˆ’1)Â = 1887 512248 533641 285992 786408 845563 122929 207882 311505 295918 668652 [i]
3. linear OA(2⁶, 7, F₂, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,2)), using
  - dual of repetition code with length 7 [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(2²¹⁹, 272, F₂, 74) (dual of [272, 53, 75]-code)	[i]	Strength Reduction
2	Linear OA(2²²⁰, 273, F₂, 75) (dual of [273, 53, 76]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²²¹, 274, F₂, 75) (dual of [274, 53, 76]-code)	[i]
4	Linear OA(2²²², 275, F₂, 75) (dual of [275, 53, 76]-code)	[i]
5	Linear OA(2²¹⁷, 270, F₂, 73) (dual of [270, 53, 74]-code)	[i]	Truncation