MinT - Information on Result #837513

Information on Result #837513

Linear OOA(5¹⁴⁵, 1585, F₅, 2, 33) (dual of [(1585, 2), 3025, 34]-NRT-code), using OOA 2-folding based on linear OA(5¹⁴⁵, 3170, F₅, 33) (dual of [3170, 3025, 34]-code), using

constructionÂ X applied to C([0,16]) âŠ‚ C([0,12]) [i] based on
1. linear OA(5¹³¹, 3126, F₅, 33) (dual of [3126, 2995, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126Â | 5¹⁰âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
2. linear OA(5¹⁰¹, 3126, F₅, 25) (dual of [3126, 3025, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126Â | 5¹⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
3. linear OA(5¹⁴, 44, F₅, 7) (dual of [44, 30, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁴, 52, F₅, 7) (dual of [52, 38, 8]-code), using
    - trace code [i] based on linear OA(25⁷, 26, F₂₅, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
      - extended Reedâ€“Solomon code RS_e(19,25) [i]
      - the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      - algebraic-geometric code AG(F,9P) with 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,6P) with 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(5¹⁴⁶, 1585, F₅, 2, 33) (dual of [(1585, 2), 3024, 34]-NRT-code)	[i]		OOA Duplication