MinT - Information on Result #2848675

Information on Result #2848675

Linear OOA(2²⁵⁶, 66, F₂, 5, 132) (dual of [(66, 5), 74, 133]-NRT-code), using strength reduction based on linear OOA(2²⁵⁶, 66, F₂, 5, 133) (dual of [(66, 5), 74, 134]-NRT-code), using

constructionÂ X applied to AG(5;F,53P) âŠ‚ AG(5;F,71P) [i] based on
1. linear OOA(2²⁰², 48, F₂, 5, 133) (dual of [(48, 5), 38, 134]-NRT-code), using algebraic-geometric NRT-code AG(5;F,53P) 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(2¹⁶⁶, 48, F₂, 5, 97) (dual of [(48, 5), 74, 98]-NRT-code), using algebraic-geometric NRT-code AG(5;F,71P) 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(2²⁵⁷, 66, F₂, 5, 132) (dual of [(66, 5), 73, 133]-NRT-code)	[i]		OOA Duplication