MinT - Information on Result #837439

Information on Result #837439

Linear OOA(5¹⁴², 1588, F₅, 2, 32) (dual of [(1588, 2), 3034, 33]-NRT-code), using OOA 2-folding based on linear OA(5¹⁴², 3176, F₅, 32) (dual of [3176, 3034, 33]-code), using

constructionÂ X applied to C_e(31) âŠ‚ C_e(22) [i] based on
1. linear OA(5¹²⁶, 3125, F₅, 32) (dual of [3125, 2999, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
2. linear OA(5⁹¹, 3125, F₅, 23) (dual of [3125, 3034, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
3. linear OA(5¹⁶, 51, F₅, 8) (dual of [51, 35, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁶, 52, F₅, 8) (dual of [52, 36, 9]-code), using
    - trace code [i] based on linear OA(25⁸, 26, F₂₅, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using
      - extended Reedâ€“Solomon code RS_e(18,25) [i]
      - algebraic-geometric code AG(F, Q+7P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
      - algebraic-geometric code AG(F, Q+5P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

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(5¹⁴⁴, 1589, F₅, 2, 32) (dual of [(1589, 2), 3034, 33]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(5¹⁴³, 1588, F₅, 2, 32) (dual of [(1588, 2), 3033, 33]-NRT-code)	[i]		OOA Duplication