MinT - Information on Result #1082607

Information on Result #1082607

Linear OOA(81⁴², 1757, F₈₁, 4, 16) (dual of [(1757, 4), 6986, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁰, 116, F₈₁, 4, 8) (dual of [(116, 4), 454, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,455P) [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
  - a function field by SÃ©mirat [i]
linear OOA(81³², 1641, F₈₁, 4, 16) (dual of [(1641, 4), 6532, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81³², 6564, F₈₁, 16) (dual of [6564, 6532, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(81³², 6566, F₈₁, 16) (dual of [6566, 6534, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(13) [i] based on
      1. linear OA(81³¹, 6561, F₈₁, 16) (dual of [6561, 6530, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(81²⁷, 6561, F₈₁, 14) (dual of [6561, 6534, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(81¹, 5, F₈₁, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 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(81⁴², 878, F₈₁, 20, 16) (dual of [(878, 20), 17518, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row