A linear block code over a field can be derived from a unit scheme. Looking at codes as structures within a unit scheme greatly extends the availability of linear block and convolutional codes and allows the construction of the codes to required length, rate, distance and type. Properties of a code emanate from properties of the unit from which it was derived. %% can thus be constructed and analysed by designating the units whose properties would give the required codes. Orthogonal units, units in group rings, Fourier/Vandermonde units and related units are used to construct and analyse linear block and convolutional codes and to construct these to predefined length, rate, distance and type. Self-dual, dual containing, quantum error-correcting and complementary dual linear block and convolutional codes are constructed. Low density parity check linear block and convolutional codes are constructed using group rings and are constructed with no short cycles in the control matrix. From a single unit, multiple codes of a required type are derivable.

翻译：域上的线性分组码可源自单位构型。将码视为单位构型内的结构，极大扩展了线性分组码与卷积码的可用范围，并允许按所需长度、码率、距离和类型构造码。码的性质源于其所源自的单位的性质，因此可通过指定具有所需性质的单位来构造和分析码。本文利用正交单位、群环中的单位、傅里叶/范德蒙德单位及相关单位，来构造和分析线性分组码与卷积码，并使其具有预定的长度、码率、距离和类型。我们构造了自对偶码、含对偶码、量子纠错码及互补对偶线性分组码与卷积码。利用群环构造了低密度奇偶校验线性分组码与卷积码，且其校验矩阵中无短环。从单个单位出发，可推导出所需类型的多个码。