MinT - Information on Result #938746

Information on Result #938746

Linear OOA(3²²⁵, 294, F₃, 2, 61) (dual of [(294, 2), 363, 62]-NRT-code), using trace code based on linear OOA(27⁷⁵, 98, F₂₇, 2, 61) (dual of [(98, 2), 121, 62]-NRT-code), using

constructionÂ X applied to AG(2;F,128P) âŠ‚ AG(2;F,132P) [i] based on
1. linear OOA(27⁷², 95, F₂₇, 2, 61) (dual of [(95, 2), 118, 62]-NRT-code), using algebraic-geometric NRT-code AG(2;F,128P) [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(27⁶⁸, 95, F₂₇, 2, 57) (dual of [(95, 2), 122, 58]-NRT-code), using algebraic-geometric NRT-code AG(2;F,132P) [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96 (see above)
3. linear OOA(27³, 3, F₂₇, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27³, 27, F₂₇, 2, 3) (dual of [(27, 2), 51, 4]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;51,27) [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		Method
1	Linear OOA(3²²⁷, 295, F₃, 2, 61) (dual of [(295, 2), 363, 62]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3²²⁶, 294, F₃, 2, 61) (dual of [(294, 2), 362, 62]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²²⁵, 147, F₃, 4, 61) (dual of [(147, 4), 363, 62]-NRT-code)	[i]	OOA Folding