  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 and
required 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 be specified to be of a particular type such 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 and infinite series of
convolutional codes with rate approaching a given rational $R$ and distance
over length approaching $2(1-R)$ are designed. The designs are algebraic and
properties, including distances, are shown algebraically. Algebraic explicit
efficient decoding methods are referenced.
