Locally repairable codes (LRCs) are a new family of erasure codes used in distributed storage systems which have attracted a great deal of interest in recent years. For an 
   linear code, if a code symbol can
            
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            Locally repairable codes (LRCs) are a new family of erasure codes used in distributed storage systems which have attracted a great deal of interest in recent years. For an 
   linear code, if a code symbol can be repaired by 
t disjoint groups of other code symbols, where each group contains at most 
r code symbols, it is said to have 
availability-  . Single-parity LRCs are LRCs with a constraint that each repairable group contains exactly one parity symbol. For an 
   single-parity LRC with 
availability-   for the information symbols (single-parity LRCs), the minimum distance satisfies 
  . In this paper, we focus on the study of single-parity LRCs with availability-
   for information symbols. Based on the standard form of generator matrices, we present a novel characterization of single-parity LRCs with availability 
  . Then, a simple and straightforward proof for the Singleton-type bound is given based on the new characterization. Some necessary conditions for optimal single-parity LRCs with availability 
   are obtained, which might provide some guidelines for optimal coding constructions.
            
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