Scalable error correction for sequential multiple data sectors in data storage device

A data storage device and method stores data in tracks that include a plurality of sectors of write data. A media erasure detection encoder/decoder (MEDC) 14 receives a set of sectors to be written sequentially on a selected track and generates error correction code (ECC) checks for each sector. A track erasure encoder/decoder (TED) 15 receives the data and the ECC checks for each sector and generates one or more cumulative weighted parity sectors per track to be recorded. The cumulatively weighted parity sectors are generated sequentially from the data and the ECC checks for each sector. The method can be used for recovering squeezed sectors in a set of sequential sectors such as used in shingled magnetic recording (SMR). The TED can use a Cauchy type track erasure correction code. A programmable set of sector symbol multipliers can iteratively generate a Cauchy matrix where the number of multipliers equals the number of parity sectors.