MinT - Information on Result #1726669

Information on Result #1726669

Linear OOA(7⁹⁹, 421, F₇, 33, 29) (dual of [(421, 33), 13794, 30]-NRT-code), using OOA 5-folding and stacking with additional row based on linear OOA(7⁹⁹, 2106, F₇, 3, 29) (dual of [(2106, 3), 6219, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(7⁹⁹, 2110, F₇, 3, 29) (dual of [(2110, 3), 6231, 30]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁹⁹, 2110, F₇, 29) (dual of [2110, 2011, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁹⁹, 2409, F₇, 29) (dual of [2409, 2310, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(25) [i] based on
      1. linear OA(7⁹⁷, 2401, F₇, 29) (dual of [2401, 2304, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 7⁴âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(7⁸⁹, 2401, F₇, 26) (dual of [2401, 2312, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 7⁴âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      3. linear OA(7², 8, F₇, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
        extended Reedâ€“Solomon code RS_e(6,7) [i]
        Hamming code H(2,7) [i]
        algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8, using the rational function field F₇(x) [i]

Mode: Linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (70, 99, 421)-net over F₇	[i]		Net Defined by OOA