MinT - Information on Result #902513

Information on Result #902513

Linear OOA(32⁹⁸, 16431, F₃₂, 2, 28) (dual of [(16431, 2), 32764, 29]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹⁵, 44, F₃₂, 2, 14) (dual of [(44, 2), 73, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,73P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
  - a function field by SÃ©mirat [i]
linear OOA(32⁸³, 16387, F₃₂, 2, 28) (dual of [(16387, 2), 32691, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁸³, 32774, F₃₂, 28) (dual of [32774, 32691, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁸³, 32775, F₃₂, 28) (dual of [32775, 32692, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(25) [i] based on
      1. linear OA(32⁸², 32768, F₃₂, 28) (dual of [32768, 32686, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(32⁷⁶, 32768, F₃₂, 26) (dual of [32768, 32692, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      3. linear OA(32¹, 7, F₃₂, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(32¹, s, F₃₂, 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(32⁹⁸, 2347, F₃₂, 30, 28) (dual of [(2347, 30), 70312, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row