MinT - Information on Result #671020

Information on Result #671020

Linear OA(128⁶⁸, 482, F₁₂₈, 37) (dual of [482, 414, 38]-code), using (u,Â u+v)-construction based on

linear OA(128²², 194, F₁₂₈, 18) (dual of [194, 172, 19]-code), using
- constructionÂ X applied to AG(F,172P) âŠ‚ AG(F,174P) [i] based on
  1. linear OA(128²¹, 191, F₁₂₈, 18) (dual of [191, 170, 19]-code), using algebraic-geometric code AG(F,172P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
    - a function field by SÃ©mirat [i]
  2. linear OA(128¹⁹, 191, F₁₂₈, 16) (dual of [191, 172, 17]-code), using algebraic-geometric code AG(F,174P) [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192 (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(128⁴⁶, 288, F₁₂₈, 37) (dual of [288, 242, 38]-code), using
- extended algebraic-geometric code AG_e(F,250P) [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, 241, F₁₂₈, 2, 37) (dual of [(241, 2), 414, 38]-NRT-code)	[i]		OOA Folding