扭曲立方码的扩展陪集首重计数器
The extended coset leader weight enumerator of a twisted cubic code
摘要：
计算了广义Reed-Solomon $[q + 1, q - 3, 5]_q$码的扩展陪集首重枚举数。计算被认为是一个有限几何问题。为此，我们需要分类的点，线和平面的射影空间下的射影，离开扭曲的立方不变。三个空间中的一条直线决定次数至多为三的有理函数，反之亦然。进一步研究了有理函数的二重点格式。扭三次曲面的一个不在密切平面上的真传递子的束给出亏格为一的曲线作为二重点方案。利用Fq-有理点上的Hasse-Weil界，证明了存在一个包含传递子的3-平面.
英文摘要：
The extended coset leader weight enumerator of the generalized Reed-Solomon $[q + 1, q - 3, 5]_q$ code is computed. The computation is considered as a question in finite geometry. For this we need the classification of the points, lines and planes in the projective three space under projectivities that leave the twisted cubic invariant. A line in three space determines a rational function of degree at most three and vice versa. Furthermore the double point scheme of a rational function is studied. The pencil of a true passant of the twisted cubic, not in an osculation plane gives a curve of genus one as double point scheme. With the Hasse-Weil bound on Fq-rational points we show that there is a 3-plane containing the passant.
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