MinT - Information on Result #1049143

Information on Result #1049143

Linear OOA(4²⁵², 164, F₄, 3, 93) (dual of [(164, 3), 240, 94]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁸⁶, 60, F₄, 3, 46) (dual of [(60, 3), 94, 47]-NRT-code), using
- constructionÂ X applied to AG(3;F,118P) âŠ‚ AG(3;F,126P) [i] based on
  1. linear OOA(4⁷⁹, 55, F₄, 3, 46) (dual of [(55, 3), 86, 47]-NRT-code), using algebraic-geometric NRT-code AG(3;F,118P) [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(4⁷¹, 55, F₄, 3, 38) (dual of [(55, 3), 94, 39]-NRT-code), using algebraic-geometric NRT-code AG(3;F,126P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
  3. linear OOA(4⁷, 5, F₄, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;8,4) [i]
linear OOA(4¹⁶⁶, 104, F₄, 3, 93) (dual of [(104, 3), 146, 94]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,218P) [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(4²⁵², 164, F₄, 3, 92) (dual of [(164, 3), 240, 93]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²⁵³, 164, F₄, 3, 93) (dual of [(164, 3), 239, 94]-NRT-code)	[i]		OOA Duplication