Abstract
Bachoc bachoc has recently introduced harmonic polynomials for binary codes. Computing these for extremal even formally self-dual codes of length 12, she found intersection numbers for such codes and showed that there are exactly three inequivalent [12,6,4] even formally self-dual codes, exactly one of which is self-dual. We prove a new theorem which gives a generator matrix for formally self-dual codes. Using the Bachoc polynomials we can obtain the intersection numbers for extremal even formally self-dual codes of length 14. These same numbers can also be obtained from the generator matrix. We show that there are precisely ten inequivalent [14,7,4] even formally self-dual codes, only one of which is self-dual.
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Fields, J.E., Gaborit, P., Huffman, W.C. et al. On the Classification of Extremal Even Formally Self-Dual Codes. Designs, Codes and Cryptography 18, 125–148 (1999). https://doi.org/10.1023/A:1008389220478
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DOI: https://doi.org/10.1023/A:1008389220478