MinT - Information on Result #671002

Information on Result #671002

Linear OA(128⁶⁸, 440, F₁₂₈, 38) (dual of [440, 372, 39]-code), using (u,Â u+v)-construction based on

linear OA(128²¹, 152, F₁₂₈, 19) (dual of [152, 131, 20]-code), using
- constructionÂ X applied to AG(F,129P) âŠ‚ AG(F,131P) [i] based on
  1. linear OA(128²⁰, 149, F₁₂₈, 19) (dual of [149, 129, 20]-code), using algebraic-geometric code AG(F,129P) [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]
  2. linear OA(128¹⁸, 149, F₁₂₈, 17) (dual of [149, 131, 18]-code), using algebraic-geometric code AG(F,131P) [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150 (see above)
  3. linear OA(128¹, 3, F₁₂₈, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(128⁴⁷, 288, F₁₂₈, 38) (dual of [288, 241, 39]-code), using
- extended algebraic-geometric code AG_e(F,249P) [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
  - a function field by SÃ©mirat [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(128⁶⁸, 220, F₁₂₈, 2, 38) (dual of [(220, 2), 372, 39]-NRT-code)	[i]		OOA Folding