MinT - Information on Result #1015115

Information on Result #1015115

Linear OOA(8¹⁵⁶, 10971, F₈, 3, 30) (dual of [(10971, 3), 32757, 31]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8²⁴, 45, F₈, 3, 15) (dual of [(45, 3), 111, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,119P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
  - an explicitly constructive algebraic function field [i]
linear OOA(8¹³², 10926, F₈, 3, 30) (dual of [(10926, 3), 32646, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8¹³², 32778, F₈, 30) (dual of [32778, 32646, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹³², 32779, F₈, 30) (dual of [32779, 32647, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(27) [i] based on
      1. linear OA(8¹³¹, 32768, F₈, 30) (dual of [32768, 32637, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(8¹²¹, 32768, F₈, 28) (dual of [32768, 32647, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(8¹, 11, F₈, 1) (dual of [11, 10, 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁵⁶, 2194, F₈, 33, 30) (dual of [(2194, 33), 72246, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row