On Linear Cyclic Codes with $\lambda$-Connected and Certain Other Checks

The article considers linear cyclic codes that correct additive errors by $\lambda$-connected checks and certain other more general checks. A necessary condition which these codes must satisfy is obtained. In particular, this condition yields certain lower bounds for the minimum number of redundant symbols in codes that correct one error by $\lambda$-connected checks. The possibility of using certain specific codes (in particular, BCH codes) for correcting errors by $\lambda$-connected checks is also considered.