MinT - Information on Result #1049107

Information on Result #1049107

Linear OOA(4²³⁷, 162, F₄, 3, 85) (dual of [(162, 3), 249, 86]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁷⁹, 58, F₄, 3, 42) (dual of [(58, 3), 95, 43]-NRT-code), using
- constructionÂ X applied to AG(3;F,122P) âŠ‚ AG(3;F,127P) [i] based on
  1. linear OOA(4⁷⁵, 55, F₄, 3, 42) (dual of [(55, 3), 90, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,122P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. linear OOA(4⁷⁰, 55, F₄, 3, 37) (dual of [(55, 3), 95, 38]-NRT-code), using algebraic-geometric NRT-code AG(3;F,127P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
  3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;8,4) [i]
linear OOA(4¹⁵⁸, 104, F₄, 3, 85) (dual of [(104, 3), 154, 86]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,226P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
  - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²³⁸, 162, F₄, 3, 85) (dual of [(162, 3), 248, 86]-NRT-code)	[i]		OOA Duplication