MinT - Information on Result #898502

Information on Result #898502

Linear OOA(16¹¹⁴, 524361, F₁₆, 2, 21) (dual of [(524361, 2), 1048608, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(16¹⁶, 65, F₁₆, 2, 10) (dual of [(65, 2), 114, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,119P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
  - the Hermitian function field over F₁₆ [i]
linear OOA(16⁹⁸, 524296, F₁₆, 2, 21) (dual of [(524296, 2), 1048494, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(16⁹⁸, 1048592, F₁₆, 21) (dual of [1048592, 1048494, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁹⁸, 1048593, F₁₆, 21) (dual of [1048593, 1048495, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(17) [i] based on
      1. linear OA(16⁹⁶, 1048576, F₁₆, 21) (dual of [1048576, 1048480, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. linear OA(16⁸¹, 1048576, F₁₆, 18) (dual of [1048576, 1048495, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      3. linear OA(16², 17, F₁₆, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
        extended Reedâ€“Solomon code RS_e(15,16) [i]
        Hamming code H(2,16) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(16¹¹⁴, 104872, F₁₆, 22, 21) (dual of [(104872, 22), 2307070, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row