New Family of Single-Error

Absfracf-A construction is given .that combines an (n, MI, &) code with an (n, Mt, de = [+(dl + l)]) code to form a (an, M1M2, dl) code. This is used to construct a new family of nongroup singleerror correcting codes of all lengths n from 2’” to 3 . 2m-1 1, for every wz 2 3. These codes have more codewords than any group code of the same length and minimum distance. A number of other nongroup codes are also obtained. Examples of the new codes are (16,2560,3) and (16,36,7) codes, both having more codewords than any comparable group code.

[1]  Morton Nadler,et al.  A 32-point n=12, d=5 code (Corresp.) , 1962, IRE Trans. Inf. Theory.

[2]  Selmer M. Johnson.  On upper bounds for unrestricted binary-error-correcting codes , 1971, IEEE Trans. Inf. Theory.

[3]  John P. Robinson,et al.  An Optimum Nonlinear Code , 1967, Inf. Control..

[4]  J. Leech.  Some Sphere Packings in Higher Space , 1964, Canadian Journal of Mathematics.

[5]  D. Slepian.  Some further theory of group codes , 1960 .

[6]  Franco P. Preparata.  A Class of Optimum Nonlinear Double-Error-Correcting Codes , 1968, Inf. Control..

[7]  N. Sloane,et al.  Sphere Packings and Error-Correcting Codes , 1971, Canadian Journal of Mathematics.

[8]  Elwyn R. Berlekamp,et al.  Algebraic coding theory , 1984, McGraw-Hill series in systems science.

[9]  Morris Plotkin,et al.  Binary codes with specified minimum distance , 1960, IRE Trans. Inf. Theory.

[10]  Marcel J. E. Golay,et al.  Binary coding , 1954, Transactions of the IRE Professional Group on Information Theory.

[11]  D. Julin,et al.  Two improved block codes , 1965 .

[12]  O. Perron,et al.  Bemerkungen über die Verteilung der quadratischen Reste , 1952 .