MinT - Information on Result #661485

Information on Result #661485

Linear OA(2²⁵⁹, 355, F₂, 77) (dual of [355, 96, 78]-code), using concatenation of two codes based on

linear OA(16⁴⁷, 71, F₁₆, 38) (dual of [71, 24, 39]-code), using
- constructionÂ X applied to AG(F,25P) âŠ‚ AG(F,29P) [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(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(16³, 7, F₁₆, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,16) or 7-cap in PG(2,16)), using
    - discarding factors / shortening the dual code based on linear OA(16³, 16, F₁₆, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
      - Reedâ€“Solomon code RS(13,16) [i]
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.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(2²⁵⁹, 355, F₂, 76) (dual of [355, 96, 77]-code)	[i]	Strength Reduction
2	Linear OA(2²⁶⁰, 356, F₂, 77) (dual of [356, 96, 78]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²⁵⁸, 354, F₂, 76) (dual of [354, 96, 77]-code)	[i]	Truncation
4	Linear OOA(2²⁵⁹, 177, F₂, 2, 77) (dual of [(177, 2), 95, 78]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2²⁵⁹, 118, F₂, 3, 77) (dual of [(118, 3), 95, 78]-NRT-code)	[i]	OOA Folding