Title :
Number of minimum-weight code words in a product code
Author_Institution :
California Institute of Technology, Jet Propulsion Laboratory, Pasadena, USA
Abstract :
It is well known that if the linear code Ci over GF(q) has ¿i words of minimum weight Wi (1 ¿ i ¿ t), then the product C = C1 ¿ C2¿¿¿Ct has minimum weight w1 w2¿Wt. In this letter it is shown that C has exactly ¿1 ¿2¿ ¿t/(q ¿ 1)t¿1 such minimum-weight code words. Moreover, if v¿C has weight w1w2¿wt then v = v1 ¿ v2 ¿ ¿ ¿ vt where vi is a word of Ci with weight wi (1 ¿i¿t).
Keywords :
codes; minimum weight code words; product code;
Journal_Title :
Electronics Letters
DOI :
10.1049/el:19780431
