MinT - Information on Result #2693947

Information on Result #2693947

Linear OOA(4²⁵⁸, 157, F₄, 3, 105) (dual of [(157, 3), 213, 106]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²⁵⁵, 156, F₄, 3, 105) (dual of [(156, 3), 213, 106]-NRT-code), using

constructionÂ X applied to AG(3;F,281P) âŠ‚ AG(3;F,317P) [i] based on
1. linear OOA(4²¹⁰, 129, F₄, 3, 105) (dual of [(129, 3), 177, 106]-NRT-code), using algebraic-geometric NRT-code AG(3;F,281P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
  - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4¹⁷⁴, 129, F₄, 3, 69) (dual of [(129, 3), 213, 70]-NRT-code), using algebraic-geometric NRT-code AG(3;F,317P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130 (see above)
3. linear OOA(4⁴⁵, 27, F₄, 3, 35) (dual of [(27, 3), 36, 36]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,45P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4²⁵⁹, 157, F₄, 3, 105) (dual of [(157, 3), 212, 106]-NRT-code)	[i]		OOA Duplication