MinT - Information on Result #899881

Information on Result #899881

Linear OOA(25⁷⁶, 7882, F₂₅, 2, 21) (dual of [(7882, 2), 15688, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(25¹⁴, 66, F₂₅, 2, 10) (dual of [(66, 2), 118, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,121P) [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(25⁶², 7816, F₂₅, 2, 21) (dual of [(7816, 2), 15570, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁶², 15632, F₂₅, 21) (dual of [15632, 15570, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(25⁶², 15633, F₂₅, 21) (dual of [15633, 15571, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(25⁶¹, 15626, F₂₅, 21) (dual of [15626, 15565, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626Â | 25⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(25⁵⁵, 15626, F₂₅, 19) (dual of [15626, 15571, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626Â | 25⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(25¹, 7, F₂₅, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(25⁷⁶, 1576, F₂₅, 22, 21) (dual of [(1576, 22), 34596, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row