MinT - Information on Result #661500

Information on Result #661500

Linear OA(4¹⁶³, 328, F₄, 51) (dual of [328, 165, 52]-code), using concatenation of two codes based on

linear OA(64²⁷, 82, F₆₄, 25) (dual of [82, 55, 26]-code), using
- constructionÂ X applied to AG(F,53P) âŠ‚ AG(F,55P) [i] based on
  1. linear OA(64²⁶, 79, F₆₄, 25) (dual of [79, 53, 26]-code), using algebraic-geometric code AG(F,53P) [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(64²⁴, 79, F₆₄, 23) (dual of [79, 55, 24]-code), using algebraic-geometric code AG(F,55P) [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		This result only	Method
1	Linear OA(4¹⁶⁴, 329, F₄, 51) (dual of [329, 165, 52]-code)	[i]		Code Embedding in Larger Space
2	Linear OOA(4¹⁶³, 164, F₄, 2, 51) (dual of [(164, 2), 165, 52]-NRT-code)	[i]		OOA Folding