MinT - Information on Result #2226762

Information on Result #2226762

Linear OA(2²⁵⁶, 344, F₂, 78) (dual of [344, 88, 79]-code), using 1 times truncation based on linear OA(2²⁵⁷, 345, F₂, 79) (dual of [345, 88, 80]-code), using

concatenation of two codes [i] based on
1. linear OA(16⁴⁷, 69, F₁₆, 39) (dual of [69, 22, 40]-code), using
  - constructionÂ X applied to AG(F,24P) âŠ‚ AG(F,27P) [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(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(16², 5, F₁₆, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
      - discarding factors / shortening the dual code based on linear OA(16², 16, F₁₆, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
        Reedâ€“Solomon code RS(14,16) [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(2²⁵⁸, 346, F₂, 78) (dual of [346, 88, 79]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²⁵⁹, 347, F₂, 78) (dual of [347, 88, 79]-code)	[i]
3	Linear OA(2²⁶⁰, 348, F₂, 78) (dual of [348, 88, 79]-code)	[i]
4	Linear OA(2²⁶⁰, 350, F₂, 78) (dual of [350, 90, 79]-code)	[i]	VarÅ¡amovâ€“Edel Lengthening
5	Linear OA(2²⁵⁹, 348, F₂, 78) (dual of [348, 89, 79]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
6	Linear OOA(2²⁵⁶, 172, F₂, 2, 78) (dual of [(172, 2), 88, 79]-NRT-code)	[i]	OOA Folding
7	Linear OOA(2²⁵⁶, 114, F₂, 3, 78) (dual of [(114, 3), 86, 79]-NRT-code)	[i]	OOA Folding