MinT - Information on Result #661515

Information on Result #661515

Linear OA(4²²⁹, 424, F₄, 75) (dual of [424, 195, 76]-code), using concatenation of two codes based on

linear OA(64⁴¹, 106, F₆₄, 37) (dual of [106, 65, 38]-code), using
- constructionÂ X applied to AG(F,65P) âŠ‚ AG(F,67P) [i] based on
  1. linear OA(64⁴⁰, 103, F₆₄, 37) (dual of [103, 63, 38]-code), using algebraic-geometric code AG(F,65P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]
  2. linear OA(64³⁸, 103, F₆₄, 35) (dual of [103, 65, 36]-code), using algebraic-geometric code AG(F,67P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104 (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 OOA(4²²⁹, 212, F₄, 2, 75) (dual of [(212, 2), 195, 76]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4²²⁹, 141, F₄, 3, 75) (dual of [(141, 3), 194, 76]-NRT-code)	[i]		OOA Folding