Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate andrequired error-correcting capability and required types. Infinite series of block codes with rate approaching a given rational $R$ with $0<R<1$ and relative distance over length approaching $(1-R)$ are designed. These can be designed over fields of given characteristic $p$ or over fields of prime order and can of of specified typessuch as (i) dual-containing under Euclidean inner product, (ii) dual-containing under Hermitian inner product, (iii) quantum error-correcting, (iv) linear complementary dual (LCD). Convolutional codes to required rate and distance are designed and infinite series of convolutional codes with rate approaching a given rational $R$ and distance over length approaching $2(1-R)$. Properties, including distances, are shown algebraically and algebraic explicit efficient decoding methods are known.

翻译：提出了设计最大距离可分离(MDS)线性块和革命代码序列的代谢方法,用于设计符合要求规格和类型的最大距离系列的代号,为要求的代号、要求的错误更正能力和要求的类型设计了代号,为接近给定合理值的1美元和距离接近1美元(1-R)的相对距离的无穷系列区代码设计了无穷区代码,这些代号可针对特定特性的域或优等域和特定种类的可变域设计,如(一) 欧几里得内产含有双层的代号,(二) 赫米里米亚内产含有双层的代号,(三) 量级错误更正,(四) 线性补充双轨(LCD) 设计了要求率和距离接近给定值的数和距离接近2美元(1-R)的无限的代号革命代号,已知了接近给定值的代号,且距离接近2美元(1-R)的代号。