MinT - Information on Result #2226689

Information on Result #2226689

Linear OA(2²⁵⁰, 334, F₂, 78) (dual of [334, 84, 79]-code), using 1 times truncation based on linear OA(2²⁵¹, 335, F₂, 79) (dual of [335, 84, 80]-code), using

concatenation of two codes [i] based on
1. linear OA(16⁴⁶, 67, F₁₆, 39) (dual of [67, 21, 40]-code), using
  - constructionÂ X applied to AG(F,24P) âŠ‚ AG(F,26P) [i] based on
    1. linear OA(16⁴⁵, 64, F₁₆, 39) (dual of [64, 19, 40]-code), using algebraic-geometric code AG(F,24P) [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(16⁴³, 64, F₁₆, 37) (dual of [64, 21, 38]-code), using algebraic-geometric code AG(F,26P) [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(2²⁵², 336, F₂, 78) (dual of [336, 84, 79]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²⁵³, 337, F₂, 78) (dual of [337, 84, 79]-code)	[i]
3	Linear OA(2²⁵⁴, 338, F₂, 78) (dual of [338, 84, 79]-code)	[i]
4	Linear OA(2²⁵⁵, 339, F₂, 78) (dual of [339, 84, 79]-code)	[i]
5	Linear OA(2²⁵⁴, 339, F₂, 78) (dual of [339, 85, 79]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
6	Linear OOA(2²⁵⁰, 167, F₂, 2, 78) (dual of [(167, 2), 84, 79]-NRT-code)	[i]	OOA Folding
7	Linear OOA(2²⁵⁰, 111, F₂, 3, 78) (dual of [(111, 3), 83, 79]-NRT-code)	[i]	OOA Folding