MinT - Information on Result #2226551

Information on Result #2226551

Linear OA(2²³⁰, 334, F₂, 68) (dual of [334, 104, 69]-code), using 1 times truncation based on linear OA(2²³¹, 335, F₂, 69) (dual of [335, 104, 70]-code), using

concatenation of two codes [i] based on
1. linear OA(16⁴¹, 67, F₁₆, 34) (dual of [67, 26, 35]-code), using
  - constructionÂ X applied to AG(F,29P) âŠ‚ AG(F,31P) [i] based on
    1. linear OA(16⁴⁰, 64, F₁₆, 34) (dual of [64, 24, 35]-code), using algebraic-geometric code AG(F,29P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]
    2. linear OA(16³⁸, 64, F₁₆, 32) (dual of [64, 26, 33]-code), using algebraic-geometric code AG(F,31P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
    3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]

Mode: Constructive and 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(2²³², 336, F₂, 68) (dual of [336, 104, 69]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²³³, 337, F₂, 68) (dual of [337, 104, 69]-code)	[i]
3	Linear OA(2²³⁴, 338, F₂, 68) (dual of [338, 104, 69]-code)	[i]
4	Linear OA(2²³⁵, 339, F₂, 68) (dual of [339, 104, 69]-code)	[i]
5	Linear OA(2²³⁴, 339, F₂, 68) (dual of [339, 105, 69]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
6	Linear OOA(2²³⁰, 167, F₂, 2, 68) (dual of [(167, 2), 104, 69]-NRT-code)	[i]	OOA Folding
7	Linear OOA(2²³⁰, 111, F₂, 3, 68) (dual of [(111, 3), 103, 69]-NRT-code)	[i]	OOA Folding