MinT - Information on Result #661544

Information on Result #661544

Linear OA(5¹⁴⁸, 210, F₅, 67) (dual of [210, 62, 68]-code), using concatenation of two codes based on

linear OA(25³⁹, 70, F₂₅, 33) (dual of [70, 31, 34]-code), using
- constructionÂ X applied to AG(F,31P) âŠ‚ AG(F,34P) [i] based on
  1. 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, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(25³⁴, 65, F₂₅, 30) (dual of [65, 31, 31]-code), using algebraic-geometric code AG(F,34P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66 (see above)
  3. linear OA(25², 5, F₂₅, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
    - discarding factors / shortening the dual code based on linear OA(25², 25, F₂₅, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
      - Reedâ€“Solomon code RS(23,25) [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, 210, F₅, 66) (dual of [210, 62, 67]-code)	[i]	Strength Reduction
2	Linear OA(5¹⁴⁹, 211, F₅, 67) (dual of [211, 62, 68]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(5¹⁵⁰, 212, F₅, 67) (dual of [212, 62, 68]-code)	[i]	Code Embedding in Larger Space
4	Linear OA(5¹⁴⁷, 209, F₅, 66) (dual of [209, 62, 67]-code)	[i]	Truncation
5	Linear OOA(5¹⁴⁸, 105, F₅, 2, 67) (dual of [(105, 2), 62, 68]-NRT-code)	[i]	OOA Folding
6	Linear OOA(5¹⁴⁸, 70, F₅, 3, 67) (dual of [(70, 3), 62, 68]-NRT-code)	[i]	OOA Folding