This short note introduces a geometric representation for binary (or ternary) sequences. The proposed representation is linked to multivariate data plotting according to the radar chart. As an illustrative example, the binary Hamming transform recently proposed is geometrically interpreted. It is shown that codewords of standard Hamming code $\mathcal{H}(N=7,k=4,d=3)$ are invariant vectors under the Hamming transform. These invariant are eigenvectors of the binary Hamming transform. The images are always inscribed in a regular polygon of unity side, resembling triangular rose petals and/or ``thorns''. A geometric representation of the ternary Golay transform, based on the extended Golay $\mathcal{G}(N=12, k=6, d=6)$ code over $\operatorname{GF}(3)$ is also showed. This approach is offered as an alternative representation of finite-length sequences over finite prime fields.
翻译:本简短注释为二进制( 或永久) 序列引入了几何表达式。 提议的表达式与根据雷达图绘制的多变量数据绘图相关。 举例来说, 最近提议的二进制 Hamming 转换是几何解释的。 显示标准 Hamming 代码 $\ mathcal{H} (N= 7, k= 4, d=3) 的代号在 Hamming 变换 ( Hamming ) 下是不可变的矢量 。 这些非变量是二进制 Hamming 变换 的代号 。 这些图像总是被刻在一个常规的多边形中, 重复三角玫瑰花瓣和/ 或“ thorns' ” 。 根据扩展的 Golay $\ mathcal{ G} (N=12, k=6, d=6) 代码, 也显示为 $\ operatorname{ GFN} (3) 。 。 这个方法是作为固定主场上定数序列的替代表示 。