MinT - Information on Result #661545

Information on Result #661545

Linear OA(5¹⁴⁸, 204, F₅, 71) (dual of [204, 56, 72]-code), using concatenation of two codes based on

linear OA(25⁴⁰, 68, F₂₅, 35) (dual of [68, 28, 36]-code), using
- constructionÂ X applied to AG(F,29P) âŠ‚ AG(F,31P) [i] based on
  1. linear OA(25³⁹, 65, F₂₅, 35) (dual of [65, 26, 36]-code), using algebraic-geometric code AG(F,29P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(25³⁷, 65, F₂₅, 33) (dual of [65, 28, 34]-code), using algebraic-geometric code AG(F,31P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (see above)
  3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(5¹, 3, F₅, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 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(5¹⁴⁸, 204, F₅, 70) (dual of [204, 56, 71]-code)	[i]	Strength Reduction
2	Linear OA(5¹⁴⁹, 205, F₅, 71) (dual of [205, 56, 72]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(5¹⁵⁰, 206, F₅, 71) (dual of [206, 56, 72]-code)	[i]	Code Embedding in Larger Space
4	Linear OA(5¹⁴⁷, 203, F₅, 70) (dual of [203, 56, 71]-code)	[i]	Truncation
5	Linear OOA(5¹⁴⁸, 102, F₅, 2, 71) (dual of [(102, 2), 56, 72]-NRT-code)	[i]	OOA Folding
6	Linear OOA(5¹⁴⁸, 68, F₅, 3, 71) (dual of [(68, 3), 56, 72]-NRT-code)	[i]	OOA Folding