MinT - Information on Result #661514

Information on Result #661514

Linear OA(4²⁰⁵, 328, F₄, 79) (dual of [328, 123, 80]-code), using concatenation of two codes based on

linear OA(64⁴¹, 82, F₆₄, 39) (dual of [82, 41, 40]-code), using
- constructionÂ X applied to AG(F,39P) âŠ‚ AG(F,41P) [i] based on
  1. linear OA(64⁴⁰, 79, F₆₄, 39) (dual of [79, 39, 40]-code), using algebraic-geometric code AG(F,39P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]
  2. linear OA(64³⁸, 79, F₆₄, 37) (dual of [79, 41, 38]-code), using algebraic-geometric code AG(F,41P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80 (see above)
  3. linear OA(64¹, 3, F₆₄, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(4¹, 4, F₄, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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(4²⁰⁵, 328, F₄, 78) (dual of [328, 123, 79]-code)	[i]	Strength Reduction
2	Linear OA(4²⁰⁶, 329, F₄, 79) (dual of [329, 123, 80]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(4²⁰⁷, 330, F₄, 79) (dual of [330, 123, 80]-code)	[i]
4	Linear OA(4²⁰⁸, 331, F₄, 79) (dual of [331, 123, 80]-code)	[i]
5	Linear OA(4²⁰⁴, 327, F₄, 78) (dual of [327, 123, 79]-code)	[i]	Truncation
6	Linear OOA(4²⁰⁵, 164, F₄, 2, 79) (dual of [(164, 2), 123, 80]-NRT-code)	[i]	OOA Folding
7	Linear OOA(4²⁰⁵, 109, F₄, 3, 79) (dual of [(109, 3), 122, 80]-NRT-code)	[i]	OOA Folding