MinT - Information on Result #661486

Information on Result #661486

Linear OA(2²⁵⁹, 335, F₂, 83) (dual of [335, 76, 84]-code), using concatenation of two codes based on

linear OA(16⁴⁸, 67, F₁₆, 41) (dual of [67, 19, 42]-code), using
- constructionÂ X applied to AG(F,22P) âŠ‚ AG(F,24P) [i] based on
  1. linear OA(16⁴⁷, 64, F₁₆, 41) (dual of [64, 17, 42]-code), using algebraic-geometric code AG(F,22P) [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(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 (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(2²⁵⁹, 335, F₂, 82) (dual of [335, 76, 83]-code)	[i]	Strength Reduction
2	Linear OA(2²⁶⁰, 336, F₂, 83) (dual of [336, 76, 84]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(2²⁵⁸, 334, F₂, 82) (dual of [334, 76, 83]-code)	[i]	Truncation
4	Linear OOA(2²⁵⁹, 167, F₂, 2, 83) (dual of [(167, 2), 75, 84]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2²⁵⁹, 111, F₂, 3, 83) (dual of [(111, 3), 74, 84]-NRT-code)	[i]	OOA Folding