Long Binary Narrow-Sense BCH Codes Are Normal

Let C be the binary narrow-sense BCH code of length where m is the order of 2 modulo n. Using characters of finite fields and a theorem of Weil, and results of Vladut-Skorobogatov and Lang-Weil we prove that the code C is normal in the non-primitive case if and in the primitive case if where the constant depends only on t. Received January 4, 1994     

On the Covering Radius of Long 5-ary BCH Codes with Minimum Distance 7

 We study S. D. Cohen’s method of estimating the covering radius of long primitive non-binary BCH codes with prime field alphabet. As an application we show that the covering radius is at most 7 for long 5-ary BCH codes with minimum distance seven. Received: November 13, 1996; revised version: March 11, 1997     

Covering Radius 1985–1994

 We survey important developments in the theory of covering radius during the period 1985–1994. We present lower bounds, constructions and upper bounds, the linear and nonlinear cases, density and asymptotic results, normality, specific classes of codes, covering radius and dual distance, tables, and open problems. Received October 28, 1994; revised version May 28, 1996