MinT - Information on Result #2295719

Information on Result #2295719

Linear OA(2²¹³, 270, F₂, 71) (dual of [270, 57, 72]-code), using adding a parity check bit based on linear OA(2²¹², 269, F₂, 70) (dual of [269, 57, 71]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(2²⁰⁷, 263, F₂, 70) (dual of [263, 56, 71]-code), using
  - 1 times truncation [i] based on linear OA(2²⁰⁸, 264, F₂, 71) (dual of [264, 56, 72]-code), using
    - concatenation of two codes [i] based on
      1. linear OA(16¹⁹, 33, F₁₆, 17) (dual of [33, 14, 18]-code), using
        extended algebraic-geometric code AG_e(F,15P) [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(2²⁰⁷, 264, F₂, 65) (dual of [264, 57, 66]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2²⁰⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 201 569979 693380 293636 105835 216803 862835 436525 255848 786371 644252 [i]
3. linear OA(2⁴, 5, F₂, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,2)), using
  - dual of repetition code with length 5 [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(2²¹³, 270, F₂, 70) (dual of [270, 57, 71]-code)	[i]	Strength Reduction
2	Linear OA(2²¹⁴, 271, F₂, 71) (dual of [271, 57, 72]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²¹⁵, 272, F₂, 71) (dual of [272, 57, 72]-code)	[i]	Code Embedding in Larger Space