MinT - Information on Result #2847694

Information on Result #2847694

Linear OOA(2²⁴⁶, 66, F₂, 5, 122) (dual of [(66, 5), 84, 123]-NRT-code), using strength reduction based on linear OOA(2²⁴⁶, 66, F₂, 5, 123) (dual of [(66, 5), 84, 124]-NRT-code), using

constructionÂ X applied to AG(5;F,58P) âŠ‚ AG(5;F,76P) [i] based on
1. linear OOA(2¹⁹², 48, F₂, 5, 123) (dual of [(48, 5), 48, 124]-NRT-code), using algebraic-geometric NRT-code AG(5;F,58P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
2. linear OOA(2¹⁵⁶, 48, F₂, 5, 87) (dual of [(48, 5), 84, 88]-NRT-code), using algebraic-geometric NRT-code AG(5;F,76P) with degPÂ =Â 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48 (see above)
3. linear OOA(2⁵⁴, 18, F₂, 5, 35) (dual of [(18, 5), 36, 36]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2⁵⁴, 19, F₂, 5, 35) (dual of [(19, 5), 41, 36]-NRT-code), using
    - algebraic-geometric NRT-code AG(5;F,59P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, 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(2²⁴⁷, 66, F₂, 5, 122) (dual of [(66, 5), 83, 123]-NRT-code)	[i]		OOA Duplication