MinT - Information on Result #669650

Information on Result #669650

Linear OA(64⁵⁸, 259, F₆₄, 33) (dual of [259, 201, 34]-code), using (u,Â u+v)-construction based on

linear OA(64¹⁸, 82, F₆₄, 16) (dual of [82, 64, 17]-code), using
- constructionÂ X applied to AG(F,62P) âŠ‚ AG(F,64P) [i] based on
  1. linear OA(64¹⁷, 79, F₆₄, 16) (dual of [79, 62, 17]-code), using algebraic-geometric code AG(F,62P) [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(64¹⁵, 79, F₆₄, 14) (dual of [79, 64, 15]-code), using algebraic-geometric code AG(F,64P) [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(64⁴⁰, 177, F₆₄, 33) (dual of [177, 137, 34]-code), using
- extended algebraic-geometric code AG_e(F,143P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(64⁵⁸, 129, F₆₄, 2, 33) (dual of [(129, 2), 200, 34]-NRT-code)	[i]		OOA Folding