Generating and using invertible, shortened Bose-Chaudhuri-Hocquenghem codewords

A system comprising:

• a memory device;
• and
• a processing device, operatively coupled with the memory device, to:
• receive a request to store user data bits to the memory device expand the user data bits and an inversion bit to bit locations of a codeword template, wherein the expanding forms expanded inversion and user data bits that collectively include additional bits to represent the user data bits and the inversion bit, wherein the inversion bit indicates whether the user data bits are inverted, wherein the codeword template maps a first set of bit positions corresponding to the user data bits and the inversion bit to a second set of bit positions corresponding to the expanded inversion and user data bits,
• generate parity bits for the expanded inversion and user data bits to form a shortened codeword, wherein the shortened codeword comprises the expanded inversion and user data bits, and the parity bits,
• compress the shortened codeword to form a compressed shortened codeword, wherein the compressed shortened codeword has fewer bits than the shortened codeword, and
• store the compressed shortened codeword in the set of memory devices.

A non-transitory machine-readable storage medium, which stores instructions that, when executed by a processor of a controller, cause the controller to:

• expand user data bits and an inversion bit to bit locations of a codeword template, wherein the expanding forms expanded inversion and user data bits that collectively include additional bits to represent the user data bits and the inversion bit, wherein the inversion bit indicates whether the user data bits are inverted, wherein the codeword template maps a first set of bit positions corresponding to the user data bits and the inversion bit to a second set of bit positions corresponding to the expanded inversion and user data bits;
• generate parity bits for the expanded inversion and user data bits to form a shortened codeword, wherein the shortened codeword comprises the expanded inversion and user data bits, and the parity bits;
• compress the shortened codeword to form a compressed shortened codeword, wherein the compressed shortened codeword has fewer bits than the shortened codeword;
• and
• store the compressed shortened codeword in a set of memory devices.