MinT - Information on Result #2226713

Information on Result #2226713

Linear OA(2²⁴⁸, 344, F₂, 74) (dual of [344, 96, 75]-code), using 1 times truncation based on linear OA(2²⁴⁹, 345, F₂, 75) (dual of [345, 96, 76]-code), using

concatenation of two codes [i] based on
1. linear OA(16⁴⁵, 69, F₁₆, 37) (dual of [69, 24, 38]-code), using
  - constructionÂ X applied to AG(F,26P) âŠ‚ AG(F,29P) [i] based on
    1. 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, using
      - the Hermitian function field over F₁₆ [i]
    2. 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 (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(2²⁵⁰, 346, F₂, 74) (dual of [346, 96, 75]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²⁵¹, 347, F₂, 74) (dual of [347, 96, 75]-code)	[i]
3	Linear OA(2²⁵², 348, F₂, 74) (dual of [348, 96, 75]-code)	[i]
4	Linear OA(2²⁵³, 349, F₂, 74) (dual of [349, 96, 75]-code)	[i]
5	Linear OA(2²⁵¹, 348, F₂, 74) (dual of [348, 97, 75]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
6	Linear OA(2²⁵³, 351, F₂, 74) (dual of [351, 98, 75]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
7	Linear OOA(2²⁴⁸, 172, F₂, 2, 74) (dual of [(172, 2), 96, 75]-NRT-code)	[i]	OOA Folding
8	Linear OOA(2²⁴⁸, 114, F₂, 3, 74) (dual of [(114, 3), 94, 75]-NRT-code)	[i]	OOA Folding