MinT - Information on Result #2226278

Information on Result #2226278

Linear OA(2²⁰⁶, 334, F₂, 56) (dual of [334, 128, 57]-code), using 1 times truncation based on linear OA(2²⁰⁷, 335, F₂, 57) (dual of [335, 128, 58]-code), using

concatenation of two codes [i] based on
1. linear OA(16³⁵, 67, F₁₆, 28) (dual of [67, 32, 29]-code), using
  - constructionÂ X applied to AG(F,35P) âŠ‚ AG(F,37P) [i] based on
    1. linear OA(16³⁴, 64, F₁₆, 28) (dual of [64, 30, 29]-code), using algebraic-geometric code AG(F,35P) [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(16³², 64, F₁₆, 26) (dual of [64, 32, 27]-code), using algebraic-geometric code AG(F,37P) [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(2²⁰⁸, 336, F₂, 56) (dual of [336, 128, 57]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²⁰⁹, 337, F₂, 56) (dual of [337, 128, 57]-code)	[i]
3	Linear OA(2²¹⁰, 338, F₂, 56) (dual of [338, 128, 57]-code)	[i]
4	Linear OA(2²¹⁰, 340, F₂, 56) (dual of [340, 130, 57]-code)	[i]	VarÅ¡amovâ€“Edel Lengthening
5	Linear OA(2²¹¹, 342, F₂, 56) (dual of [342, 131, 57]-code)	[i]	VarÅ¡amovâ€“Edel Lengthening
6	Linear OA(2²⁰⁹, 338, F₂, 56) (dual of [338, 129, 57]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
7	Linear OOA(2²⁰⁶, 167, F₂, 2, 56) (dual of [(167, 2), 128, 57]-NRT-code)	[i]	OOA Folding
8	Linear OOA(2²⁰⁶, 111, F₂, 3, 56) (dual of [(111, 3), 127, 57]-NRT-code)	[i]	OOA Folding