A cyclic code
is a code whose words are obtained by a permutation of a code word.
This implies that C is a linear cyclic code
In fact, a row-cyclic array code C of order m x s turns out to be [mathematical expression not reproducible] where each [C.sub.i] is a classical cyclic code
of length s.
When the ideal does not contain any smaller nonzero ideal, the corresponding cyclic code
C is called a minimal or an irreducible code.
In the CI-CDI system, simple error correcting codes can be used, such as cyclic code
([n.sub.c], [k.sub.c]), which is capable of correcting burst errors no more than 2 bits.
Keywords Quaternary cyclic code
, self-orthogonal code, quantum error-correcting code.
In particular, Jacques Wolfmann studied within this framework the notion of cyclic code
(code which is invariant by the action of the cyclic group of permutations: particular case of affine groups).
The essential quality of a cyclic code
is that any cyclic permutation or end-around shift of a code word results in another code word.
If G is cyclic, this code is called a cyclic code
, a code which is invariant under the right cyclic shift.
He covers linear codes over finite fields, cyclic codes
over finite fields, designs and codes, designs of binary Reed-Muller codes, affine invariant codes and their designs, weights in some BCH codes over GF(q), designs from four types of linear codes, designs from primitive BCH codes, designs from codes with regularity, designs from QR and self-dual codes, designs from arc and MDS codes, designs from ovoid codes, and quasi-symmetric designs from bent codes.
In this paper, we will focus on one specific type of LDPC codes, namely the difference-set cyclic codes
(DSCCs), which is widely used in the Japanese teletext system or FM multiplex broadcasting systems.