MinT - Information on Result #661455

Information on Result #661455

Linear OA(2²⁰³, 335, F₂, 55) (dual of [335, 132, 56]-code), using concatenation of two codes based on

linear OA(16³⁴, 67, F₁₆, 27) (dual of [67, 33, 28]-code), using
- constructionÂ X applied to AG(F,36P) âŠ‚ AG(F,38P) [i] based on
  1. linear OA(16³³, 64, F₁₆, 27) (dual of [64, 31, 28]-code), using algebraic-geometric code AG(F,36P) [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(16³¹, 64, F₁₆, 25) (dual of [64, 33, 26]-code), using algebraic-geometric code AG(F,38P) [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]
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(2²⁰³, 335, F₂, 54) (dual of [335, 132, 55]-code)	[i]	Strength Reduction
2	Linear OA(2²⁰⁴, 336, F₂, 55) (dual of [336, 132, 56]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²⁰⁵, 337, F₂, 55) (dual of [337, 132, 56]-code)	[i]
4	Linear OA(2²⁰⁶, 338, F₂, 55) (dual of [338, 132, 56]-code)	[i]
5	Linear OA(2²⁰², 334, F₂, 54) (dual of [334, 132, 55]-code)	[i]	Truncation
6	Linear OOA(2²⁰³, 167, F₂, 2, 55) (dual of [(167, 2), 131, 56]-NRT-code)	[i]	OOA Folding
7	Linear OOA(2²⁰³, 111, F₂, 3, 55) (dual of [(111, 3), 130, 56]-NRT-code)	[i]	OOA Folding