Some Classes of Punctured Codes

Fori∈ {1, 2}, letCibe an [n,ki,di] cyclic code over the finite field Fq. The (C1,C1+C2)-construction produces [2n,k1+k2]qquasi-cyclic (QC) codes with index 2, which have three types of codewords, i.e., (c1,c1), (0,c2) and (c1,c1+c2). In this paper, we firstly investigate the weight distributions of the QC codes (C1,C1+C2). By deleting coordinates onC1andC1+C2, we obtain several classes of linear codes with the forms (CTp,C1+C2) and (CTp, (C1+C2)Ts), whereTpandTsare sets of coordinates, and determine their weight enumerators in some cases. All these codes are optimal with respect to the Griesmer bound, and can produce new few-weight linear codes after comparing with some recent works. Finally, we analyze the minimum locality of the duals of some punctured codes. Two classes ofd-optimal andk-optimal locally recoverable codes are constructed.