I don't know whether this piece is correct or not, neither do I know if it works at all, but this is definitely the most complete version I managed to find in my code clutter.

l3.java

import java.util.Arrays;
import java.util.stream.IntStream;
 
 
public class Main {
	final static int GMOD = 0x8000;
	final static int MOD = 0x8003;
	final static int DEG = 15;
	final static int[] f1 = new int[GMOD];
	static int[][] wf1;
	final static int pow1 = (1 << 7) + 1;
	//	final static int pow1 = 257;
	final static int[] f2 = new int[GMOD];
	static int[][] wf2;
	final static int pow2 = (1 << 5) + 1;
//	final static int pow2 = 513;
 
	static {
		for (int x = 0; x < GMOD; x++) {
			f1[x] = pow(x, pow1, MOD);
			f2[x] = pow(x, pow2, MOD);
		}
		wf1 = fftWmod(f1);
		wf2 = fftWmod(f2);
	}
 
	static int mul(int a, int b, int mod) {
		int c = 0;
		for (int i = 14; i > 0; i--) {
			if (((b >> i) & 1) != 0) {
				c ^= a;
			}
 
			c <<= 1;
 
			if ((c & GMOD) != 0) {
				c ^= mod;
			}
		}
		if ((b & 1) != 0) {
			c ^= a;
		}
 
		return c;
	}
 
	static int deg(int a) {
		return a == 0 ? 0 : 63 - Long.numberOfLeadingZeros(a);
	}
 
	static int pow(int x, int m, int mod) {
		int a = 1;
		int j;
		for (j = 14; j >= 0; --j) {
			a = mul(a, a, mod);
			if (((m >>> j) & 1) != 0) {
				a = mul(a, x, mod);
			}
		}
		return a;
	}
 
	static int mod(int q, int p) {
		int k = deg(q);
		int n = deg(p);
		while (k >= n) {
			k = deg(q);
			q ^= p << (k - n);
		}
		return q;
	}
 
	static int add(int a, int b) {
		return a ^ b;
	}
 
	static int s(String val) {
		return Integer.parseInt(val, 2);
	}
 
	static double maxDiffPr(int[] f) {
 
		int globalMax = 0;
 
		for (int a = 1; a < GMOD; a++) {
			int[] b = new int[GMOD];
 
			for (int x = 0; x < GMOD; x++) {
				b[f[x] ^ f[x ^ a]]++;
			}
 
			globalMax = Math.max(globalMax, IntStream.of(b).parallel().max().getAsInt());
		}
 
		return globalMax;
	}
 
	static int[][] fftWmod(int[] f) {
		int[][] coeffs = new int[DEG][GMOD];
		for (int i = 0; i < DEG; i++) {
			coeffs[i] = new int[GMOD];
		}
 
		for (int x = 0; x < GMOD; x++) {
			for(int i = 0; i < DEG; i++) {
				coeffs[i][x] = ((f[x] >>> i) & 1) != 0 ? -1 : 1;
			}
		}
 
		for (int i = 0, mask = 1; i < DEG; i++, mask <<= 1) {
			for (int x = 0; x < GMOD; x++) {
				if ((x & mask) != 0) {
					for (int j = 0; j < DEG; j++) {
						coeffs[j][x ^ mask] = coeffs[j][x ^ mask] + coeffs[j][x];
						coeffs[j][x] = coeffs[j][x ^ mask] - 2 * coeffs[j][x];
					}
				}
			}
		}
		return coeffs;
	}
 
	static void spreadFac(int[] f) {
		int[][] k = new int[DEG][DEG];
		for (int i = 0; i < DEG; i++) {
			k[i] = new int[DEG];
		}
 
		for (int x = 0; x < GMOD; x++) {
			for (int j = 0; j < DEG; j++) {
				for (int i = 0; i < DEG; i++) {
					k[j][i] += ((f[x] ^ f[x ^ (1 << i)]) >> j) & 1;
				}
			}
		}
 
		for (int i = 0; i < DEG; i++) {
			System.out.printf("ES[%d]: %s\n", i, Arrays.toString(k[i]));
		}
	}
 
	static void disbal(int[] f) {
		int[] disb = new int[DEG];
 
		for (int i = 0; i < GMOD; ++i) {
			for (int j = 0; j < DEG; ++j) {
				disb[j] += ((f[i] >> j) & 1);
			}
		}
 
		for (int j = 0; j < DEG; ++j) {
			System.out.printf("d[%d] = %d\n", j, Math.abs(2 * disb[j] - GMOD));
		}
	}
 
	static int[] disbalXor(int[] f, int a) {
		int[] disb = new int[DEG];
 
		for (int i = 0; i < GMOD; ++i) {
			for (int j = 0; j < DEG; ++j) {
				disb[j] += ((f[i] >> j) & 1) ^ ((f[i ^ a] >> j) & 1);
			}
		}
 
		for (int j = 0; j < DEG; ++j) {
			disb[j] = Math.abs(2 * disb[j] - GMOD);
		}
		return disb;
	}
 
	static void avgSprFac(int[] f) {
		int[] k = new int[DEG];
 
		for (int x = 0; x < GMOD; x++) {
			for (int j = 0; j < DEG; j++) {
				k[j] += Integer.bitCount(f[x] ^ f[x ^ (1 << j)]);
			}
		}
 
		for (int i = 0; i < DEG; i++) {
			System.out.printf("AE[%d] = %d\n", i, k[i]);
		}
	}
 
	static int[] zhCfts(int[] f) {
		int[] coeffs = Arrays.copyOf(f, GMOD);
 
		for (int i = 0, mask = 1; i < DEG; i++, mask <<= 1) {
			for (int x = 0; x < GMOD; x++) {
				if ((x & mask) != 0) {
					coeffs[x] = coeffs[x ^ mask] ^ coeffs[x];
				}
			}
		}
 
		return coeffs;
	}
 
	static int zhDeg(int[] zhCoeffs) {
		if(zhCoeffs[GMOD - 1] != 0) {
			return DEG;
		}
 
		for(int i = 0, mask = 1; i < DEG; i++, mask <<= 1) {
			if(zhCoeffs[(GMOD - 1) ^ mask] != 0) {
				return DEG - 1;
			}
		}
 
		int max = 0;
		for(int x = 0; x < GMOD - 1; x++) {
			int pop = Integer.bitCount(x);
			if(zhCoeffs[x] != 0 &&  pop > max) {
				max = pop;
			}
		}
 
		return max;
	}
 
	static void nl(int[][] wf) {
		for (int i = 0; i < DEG; i++) {
			int max = 0;
			for (int x = 0; x < GMOD; x++) {
				if (max < wf[i][x]) {
					max = wf[i][x];
				}
			}
			System.out.printf("nl[%d] = %d\n", i, (GMOD - max) >>> 1);
		}
	}
 
	static void corrImm(int[/*DEG*/][/*GMOD*/] wf) {
		for (int i = 0; i < DEG; i++) { // i-th coord. fn
			int k;
			boolean isK = true;
			for (k = 0; k < DEG && isK; k++) {
				for (int w = 0; w < GMOD && isK; w++) {
					if (Integer.bitCount(w) >= 1 && Integer.bitCount(w) <= k) {
						if (wf[i][w] != 0) {
							isK = false;
						}
					}
				}
				if (!isK) {
					System.out.printf("f[%d]: %d\n", i, k - 1);
				}
			}
		}
	}
 
	static void strictAvlCrit(int[] f) {
		boolean[] satisfies = new boolean[DEG];
		for (int a = 1; a < GMOD; a <<= 1) {
			int[] disbal = disbalXor(f, a);
			for (int i = 0; i < DEG; i++) {
				satisfies[i] = (disbal[i] == 0);
			}
		}
		for (int i = 0; i < DEG; i++) {
			System.out.println(i + " satisfies ? " + satisfies[i]);
		}
	}
 
	public static void main(String[] args) {
		System.out.println("дисбаланс f1");
		disbal(f1);
		System.out.println("дисбаланс f2");
		disbal(f2);
		System.out.println("распространение ошибки f1");
		spreadFac(f1);
		System.out.println("распространение ошибки f2");
		spreadFac(f2);
		System.out.println("стр. ЛК в ср. f1");
		avgSprFac(f1);
		System.out.println("стр. ЛК в ср. f2");
		avgSprFac(f2);
		System.out.println("макс. дифф. вер-сть f1");
		System.out.println(maxDiffPr(f1));
		System.out.println("макс. дифф. вер-сть f2");
		System.out.println(maxDiffPr(f2));
		System.out.println("ст. п-ма Ж-на f1");
		System.out.println(zhDeg(zhCfts(f1)));
		System.out.println("ст. п-ма Ж-на f2");
		System.out.println(zhDeg(zhCfts(f2)));
		System.out.println("нелинейность f1");
		nl(wf1);
		System.out.println("нелинейность f2");
		nl(wf2);
		System.out.println("корр. имм-т f1");
		corrImm(wf1);
		System.out.println("корр. имм-т f2");
		corrImm(wf2);
		System.out.println("стр. лав. крит. f1");
		strictAvlCrit(f1);
		System.out.println("стр. лав. крит. f2");
		strictAvlCrit(f2);
	}
}