MinT - Information on Result #1014972

Information on Result #1014972

Linear OOA(8¹⁶⁴, 699077, F₈, 3, 25) (dual of [(699077, 3), 2097067, 26]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁵, 24, F₈, 3, 12) (dual of [(24, 3), 57, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,59P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OOA(8¹⁴⁹, 699053, F₈, 3, 25) (dual of [(699053, 3), 2097010, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹⁴⁹, 2097159, F₈, 25) (dual of [2097159, 2097010, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹⁴⁹, 2097160, F₈, 25) (dual of [2097160, 2097011, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [i] based on
      1. linear OA(8¹⁴⁸, 2097152, F₈, 25) (dual of [2097152, 2097004, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(8¹⁴¹, 2097152, F₈, 23) (dual of [2097152, 2097011, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(8¹, 8, F₈, 1) (dual of [8, 7, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

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(8¹⁶⁴, 174769, F₈, 27, 25) (dual of [(174769, 27), 4718599, 26]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row