MinT - Information on Result #2226663

Information on Result #2226663

Linear OA(2²⁴⁶, 334, F₂, 76) (dual of [334, 88, 77]-code), using 1 times truncation based on linear OA(2²⁴⁷, 335, F₂, 77) (dual of [335, 88, 78]-code), using

concatenation of two codes [i] based on
1. linear OA(16⁴⁵, 67, F₁₆, 38) (dual of [67, 22, 39]-code), using
  - constructionÂ X applied to AG(F,25P) âŠ‚ AG(F,27P) [i] based on
    1. linear OA(16⁴⁴, 64, F₁₆, 38) (dual of [64, 20, 39]-code), using algebraic-geometric code AG(F,25P) [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(16⁴², 64, F₁₆, 36) (dual of [64, 22, 37]-code), using algebraic-geometric code AG(F,27P) [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(2²⁴⁸, 336, F₂, 76) (dual of [336, 88, 77]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²⁴⁹, 337, F₂, 76) (dual of [337, 88, 77]-code)	[i]
3	Linear OA(2²⁵⁰, 338, F₂, 76) (dual of [338, 88, 77]-code)	[i]
4	Linear OA(2²⁵¹, 339, F₂, 76) (dual of [339, 88, 77]-code)	[i]
5	Linear OA(2²⁵⁰, 339, F₂, 76) (dual of [339, 89, 77]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
6	Linear OOA(2²⁴⁶, 167, F₂, 2, 76) (dual of [(167, 2), 88, 77]-NRT-code)	[i]	OOA Folding
7	Linear OOA(2²⁴⁶, 111, F₂, 3, 76) (dual of [(111, 3), 87, 77]-NRT-code)	[i]	OOA Folding